SAT OwlQuestion bank / Algebra
SAT Systems of two linear equations in two variables practice questions
Solve systems by substitution or elimination, and recognize when a system has no solution or infinitely many. Below are 20 free practice questions sorted from easy to hard. Open one to answer it and see the explanation.
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Question 1
x + y = 10 x - y = 4 What is the value of x in the solution to the system of equations above?EasyQuestion 2
y = 3x 2x + y = 25 If (x, y) is the solution to the system of equations, what is the value of y?EasyQuestion 3
What is the solution (x, y) to the system y = x + 2 and y = -2x + 11?EasyQuestion 4
A farm has only chickens and goats. Together the animals have 30 heads and 84 legs. Each chicken has 2 legs and each goaEasyQuestion 5
2x + 3y = 13 x = 2 What is the value of y in the solution to the system of equations above?EasyQuestion 6
3x + 2y = 16 x - 2y = 0 What is the value of x in the solution to the system of equations above?EasyQuestion 7
4x - y = 10 2x + 3y = 26 If (x, y) is the solution to the system of equations, what is the value of x + y?MediumQuestion 8
A museum sold 150 tickets in one day. Adult tickets cost 14 and student tickets cost 9. The museum collected 1,750$ fromMediumQuestion 9
5x + 2y = 31 3x - 2y = 9 If (x, y) is the solution to the system of equations, what is the value of xy?MediumQuestion 10
6x - 4y = 10 3x - 2y = 5 How many solutions does the system of equations above have?MediumQuestion 11
2x + ky = 8 4x + 10y = 3 In the system of equations above, k is a constant. For what value of k does the system have no MediumQuestion 12
In the xy-plane, the line y = mx + 4, where m is a constant, intersects the line y = 2x - 1 at the point where x = 5. WhMediumQuestion 13
12x + 13y = 7 x - y = 4 What is the value of x in the solution to the system of equations above?MediumQuestion 14
Kai invested a total of 5,000 in two accounts. One account earns 3% simple annual interest and the other earns 5% simpleMediumQuestion 15
ax + 3y = 12 4x + 6y = b In the system of equations above, a and b are constants. If the system has infinitely many soluHardQuestion 16
3x - 5y = 7 kx + 10y = 4 In the system of equations above, k is a constant. For what value of k does the system have no HardQuestion 17
In the xy-plane, the lines y = 4x - 9 and y = -2x + c, where c is a constant, intersect at the point (h, k). If k = 2h, HardQuestion 18
0.2x + 0.5y = 7.1 0.3x - 0.4y = -2 If (x, y) is the solution to the system of equations above, what is the value of 5x +HardQuestion 19
kx + 2y = 7 8x + ky = 14 In the system of equations above, k is a constant. For which of the following values of k does HardQuestion 20
A store ships candles in small boxes that hold 6 candles each and large boxes that hold 15 candles each. One shipment coHard
x + y = 10 x - y = 4 What is the value of x in the solution to the system of equations above?EasyQuestion 2
y = 3x 2x + y = 25 If (x, y) is the solution to the system of equations, what is the value of y?EasyQuestion 3
What is the solution (x, y) to the system y = x + 2 and y = -2x + 11?EasyQuestion 4
A farm has only chickens and goats. Together the animals have 30 heads and 84 legs. Each chicken has 2 legs and each goaEasyQuestion 5
2x + 3y = 13 x = 2 What is the value of y in the solution to the system of equations above?EasyQuestion 6
3x + 2y = 16 x - 2y = 0 What is the value of x in the solution to the system of equations above?EasyQuestion 7
4x - y = 10 2x + 3y = 26 If (x, y) is the solution to the system of equations, what is the value of x + y?MediumQuestion 8
A museum sold 150 tickets in one day. Adult tickets cost 14 and student tickets cost 9. The museum collected 1,750$ fromMediumQuestion 9
5x + 2y = 31 3x - 2y = 9 If (x, y) is the solution to the system of equations, what is the value of xy?MediumQuestion 10
6x - 4y = 10 3x - 2y = 5 How many solutions does the system of equations above have?MediumQuestion 11
2x + ky = 8 4x + 10y = 3 In the system of equations above, k is a constant. For what value of k does the system have no MediumQuestion 12
In the xy-plane, the line y = mx + 4, where m is a constant, intersects the line y = 2x - 1 at the point where x = 5. WhMediumQuestion 13
12x + 13y = 7 x - y = 4 What is the value of x in the solution to the system of equations above?MediumQuestion 14
Kai invested a total of 5,000 in two accounts. One account earns 3% simple annual interest and the other earns 5% simpleMediumQuestion 15
ax + 3y = 12 4x + 6y = b In the system of equations above, a and b are constants. If the system has infinitely many soluHardQuestion 16
3x - 5y = 7 kx + 10y = 4 In the system of equations above, k is a constant. For what value of k does the system have no HardQuestion 17
In the xy-plane, the lines y = 4x - 9 and y = -2x + c, where c is a constant, intersect at the point (h, k). If k = 2h, HardQuestion 18
0.2x + 0.5y = 7.1 0.3x - 0.4y = -2 If (x, y) is the solution to the system of equations above, what is the value of 5x +HardQuestion 19
kx + 2y = 7 8x + ky = 14 In the system of equations above, k is a constant. For which of the following values of k does HardQuestion 20
A store ships candles in small boxes that hold 6 candles each and large boxes that hold 15 candles each. One shipment coHard