SAT Algebra practice questions
Linear equations, systems, inequalities and functions — the largest single slice of the Digital SAT Math section.
71 free questions, each with a full worked solution and an explanation of what each wrong answer means.
Practise this domain adaptively →Easy (19)
- Linear equations in one variable
If 3x + 7 = 22, what is the value of x? - Linear equations in one variable
If x/4 = 9, what is the value of x? - Evaluating linear functions
The function f is defined by f(x) = 6x − 5. What is the value of f(3)? - Solving a literal equation (rearranging a formula)
The perimeter P of a rectangle with length l and width w is given by P = 2l + 2w. Which of the following expresses w in … - Writing a linear function from a table of values
Which equation defines the function f? - Finding the x-intercept of a line
In the xy-plane, the graph of the equation y = 4x − 12 crosses the x-axis at the point (a, 0). What is the value of a? - Solving a two-step linear equation containing a fraction
If (x − 5)/3 = 6, what is the value of x? - Solve a system by elimination in context
How many pounds of clay are used to make one mug? - Solve a system by substitution in context
How many medical kits does the team prepare? - Set up a system from a word problem
Which system of equations represents this situation? - Solve a system by elimination in context
What is the cost, in dollars, of one bag of flour? - Solve a system from a counting word problem
How many pairs does the team own? - Writing a one-variable inequality from context
Which inequality represents the possible numbers n of layers the scientist can analyze in the available laboratory time? - Solving a linear inequality for a maximum whole number
What is the greatest number of solar panels the town can install without exceeding its budget? - Testing ordered pairs in a system of inequalities
Which ordered pair (x, y) satisfies both conditions? - Interpreting a linear inequality to find a minimum count
What is the least number of timed intervals the team must complete to meet the coach's requirement? - Find the constant giving no solution
In the xy-plane, the system of equations 4x + 3y = 12 and kx + 6y = 30, where k is a constant, has no solution. What is … - Solving a one-variable inequality and interpreting the maximum
What is the greatest number of remaining sections the rider can complete without exceeding the 150-minute limit? - Solving a strict inequality for a least whole number
What is the least number of quilts the guild must sell for its profit to be more than $1,000?
Easy–Medium (14)
- Slope of a line
A line passes through the points (0, 3) and (2, 7). What is the slope of the line? - Linear models from context
A gym charges a $25 one-time signup fee plus $15 per month. Which equation gives the total cost C, in dollars, for m mon… - Linear equations with variables on both sides
If 5(x − 2) = 3x + 4, what is the value of x? - Linear equations from context
A taxi charges a $3.50 base fare plus $2.25 per mile. If a ride costs $19.25 total, how many miles was the ride? - Linear equations in two variables
The equation of a line is 3x + 2y = 12. What is the y-coordinate of the point where the line crosses the y-axis? - Linear equations in two variables
A line in the xy-plane passes through the points (1, 5) and (4, 11). What is the y-intercept of the line? - Solving a linear equation in one variable with a fractional coefficient
If (2/3)x − 5 = 7, what is the value of x? - Equations of parallel lines in the xy-plane
In the xy-plane, line m is parallel to the line with equation y = −3x + 5 and passes through the point (2, 1). If the eq… - Set up and solve a two-variable system
How many brain coral colonies did the biologist count? - Solve a cost-and-count system from context
How many child tickets were sold on Saturday? - Solve a system arising from a training plan
How many long runs does the plan call for that week? - Translate a context into a system of equations
Which system of equations represents this situation? - Find the constant making a system inconsistent
In the xy-plane, the system of equations 2x - 5y = 9 and ax + 15y = 4, where a is a constant, has no solution. What is t… - Use elimination to find one unknown quantity
What is the cost, in dollars, of one poster board?
Medium (7)
- Systems of linear equations
A system: 2x + y = 11 and x − y = 1. What is the value of x + y? - Solving linear inequalities
Which of the following describes all solutions to 4x − 9 ≤ 2x + 5? - Interpreting linear models
A phone's battery percentage is modeled by P = 100 − 8t, where t is the number of hours since it was unplugged. What doe… - Systems by substitution
If y = 2x − 1 and 3x + y = 14, what is the value of x? - Absolute value equations
If |2x − 3| = 7, what is the sum of all possible values of x? - Parallel and perpendicular lines
Line k has equation y = (2/3)x + 1. Which equation represents a line perpendicular to line k? - Systems of linear equations
At a bakery, 2 muffins and 3 cookies cost $13, while 4 muffins and 1 cookie cost $16. What is the cost, in dollars, of o…
Hard (19)
- Linear inequalities
For how many integer values of x is −2 < (x − 5)/3 ≤ 1 true? - Systems with infinitely many solutions
The system 2x + 3y = 6 and 4x + 6y = k has infinitely many solutions. What is the value of k? - Absolute value inequalities
Which of the following is the complete solution set to |x − 4| < 6? - Systems of linear inequalities
A student has $40 to spend on notebooks costing $4 each and pens costing $2 each, and wants at least 12 items total. If … - Linear inequalities in one variable (comparing two linear models)
What is the least whole number of minutes of international calling in a month for which the total monthly cost of Plan A… - Systems of two linear equations in a mixture context
How many liters of the 30% acid solution did the technician use? - Building and applying a linear function from two data points
Assuming the candle continues to burn at this rate, how many hours after it is lit will the candle's height be 6.0 centi… - Build and solve a linear equation from three related lengths
What is the length, in miles, of the Summit Trail? - Solve a linear equation with fractions on both sides
What value of n satisfies the equation? - Choose a constant so a linear equation has no solution
For what value of k is there no value of s for which the two expressions are equal? - Build a linear equation from fractional parts of a total
How many textiles are in the entire collection? - Choose a constant so a linear equation has infinitely many solutions
For what value of a do the two expressions give the same amount of water for every value of w? - Build and solve an equation comparing two multi-day rate plans
How many miles did she drive? - Write equation of perpendicular line through a point
Which equation represents the new trail in the xy-plane? - Find missing coordinate using perpendicular slope
A second route is represented by a line that passes through the points (-3, 8) and (5, k) and is perpendicular to the su… - Determine coefficient making two lines perpendicular
What is the value of k? - Find y-intercept of a parallel line
What is the y-coordinate of the y-intercept of the line representing the second corridor? - Build linear equation from two data points
Which equation gives the altitude a, in meters, of the balloon t minutes after it is released? - Find x-intercept of a perpendicular line
What is the x-coordinate of the x-intercept of the line representing the second transect?
Very hard (12)
- Systems with no solution
For what value of c does the system 3x − 2y = 8 and 9x + cy = 5 have no solution? - Systems of linear equations
In the system 5x + 4y = 32 and 3x − 2y = 6, what is the value of 8x + 2y? - Absolute value inequalities with unknown constants
The solution set of the inequality |ax − b| ≤ 6, where a and b are constants and a > 0, is 3 ≤ x ≤ 9. What is the value … - Linear functions from a constant difference condition
The function f is linear, and for every value of x, f(x + 2) − f(x) = 6. If f(5) = 4, what is the value of f(0)? - Systems of linear equations with an added constraint on the solution
In the system of equations 2x + 3y = 12 and 5x − 2y = k, where k is a constant, the solution (x, y) satisfies x = y. Wha… - Conditions for a system to have infinitely many solutions
In the xy-plane, the system of equations kx + 6y = 12 and 2x + (k − 1)y = 6, where k is a constant, has infinitely many … - Build and solve fractional linear equation from context
What is the value of t? - Model two-rate total with one linear equation
How many centimeters long is the upper section of the core? - Find parameter making a linear equation have no solution
What is the value of k? - Find parameter giving infinitely many solutions
If the two expressions give the same damage for every value of L, what is the value of c? - Solve equal-cost equation then compute requested total
What is that total cost? - Solve linear equation with fractional parts of unknown
What is the value of c?
Not affiliated with the College Board. SAT is a trademark of the College Board.