PRACTICE QUESTIONS ON SOLVING SYSTEM OF EQUATIONS FOR SAT

Problem 1 :

3x + 4y = -23

2y - x = -19

What is the solution (x, y) to the system of equations above ?

A)  (-5, -2)       B)  (3, -8)       C)  (4, -6)     D)   (9, -6)

Solution

Problem 2 :

x + y = 0

3x - 2y = 10

Which of the following ordered pairs (x, y) satisfies the system of equations above ?

A)  (3, -2)  B)  (2, -2)   C)   (-2, 2)   D)   (-2, -2)

Solution

Problem 3 :

ax + by = 12

2x + 8y = 60

In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a/b ?

Solution

Problem 4 :

y = 3

y = ax² + b

In the system of equations above, a and b are constants. For which of the following values of  a and b does the system of equations have exactly two real solutions ?

A)  a = -2, b = 2        B) a = -2, b = 4 

C)  a = 2, b = 4          D)  a = 4, b = 3

Solution

Problem 5 :

x + y = -9

x + 2y = -25

According to the system of equations above, what is the value of x ?

Solution

Problem 6 :

x + y = 29

x + 2y = 12

If the ordered pair (x, y) is the solution to the system of equations above, what is the value of y ?

A)  -17      B)  12      C)  46      D)  75

Solution

Problem 7 :

4x - 2y + 3 = 8

3x + 6y = 8y - x + 5

How many solutions does the system of equations shown above have ?

A)  0      B)  1       C)   2      D) Infinitely many

Solution

Problem 8 :

If

5b = 6a + 16 and 9a = 7b - 20

then what is the value of 3a - 2b ?

A)   -8      B)   -4       C)   4      D)  8

Solution

Problem 9 :

If the ordered pair (x, y) satisfies the system of equations above, what is the value of y ?

A)  0      B)  7      C)  10      D)  11

Solution

Problem 10 :

2x - 3y = -3

-12 = -4x + y

In what quadrant will the lines represented by the equations above intersect ?

A) Quadrant I   B)  Quadrant II  C) Quadrant III 

D)  Quadrant IV

Solution

1)  (3, -8)

2)  (2, -2)

3)  1/4

4)   a = -2, b = 4, option B

5)  y = -16

6)  y = -17

7)  infinitely many solutions

8)  3a - 2b = -4

9)  y = 11

10)  I Quadrant