SAT PRACTICE PROBLEMS ON SOLVING SYSTEM OF EQUATIONS

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:

3x + 4y = -23 ---> (1)

2y - x = -19 ---> (2)

Multiplying eq (2) with 3, we get

-3x + 6y = -57 ---> (3)

Adding eq (1) and (3), we get

10y = -80

y = -8

Substituting y = -8 in eq (2)

-16 - x = -19

-x = -3

x = 3

Hence the solution is (3, -8)

So, option (B) is correct.

Problem 2 :

x + y = -9

x + 2y = -25

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

Solution:

x + y = -9 ---> (1)

x + 2y = -25 ---> (2)

x + y = -9

y = -9 - x

Substituting y = -9 - x in (2)

x + 2(-9 - x) = -25

x - 18 - 2x = -25

-x - 18 = -25

-x = -25 + 18

-x = -7

x = 7

So, the value x is 7.

Problem 3 :

The system of equations above has solution (x, y). What is the value of x?

A) 3       B) 7/2     C) 4       D) 6

Solution:

So, option (D) is correct.

Problem 4 :

-3x + 4y = 20

6x + 3y = 15

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

Solution:

-3x + 4y = 20 ---> (1)

6x + 3y = 15 ---> (2)

Multiplying eq (1) by 2, we get

-6x + 8y = 40 ---> (3)

Adding eq (2) and (3), we get

11y = 55

y = 5

By applying y = 5 in (1),

-3x + 4(5) = 20

-3x + 20 = 20

-3x = 0

x = 0

So, value of x is 0.

Problem 5 :

x/y = 6

4(y + 1) = x

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

Solution:

Problem 6 :

kx - 3y = 4

4x - 5y = 7

In the system of equations above, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?

Solution:

kx - 3y = 4 ---> (1)

4x - 5y = 7 ---> (2)

When the system of equation will have no solution, they will not intersect each other and they must be parallel. If the lines are parallel their slopes will be equal.

k/3 = 4/5

k = 12/5

So, option (A) is correct.

Problem 7 :

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:

x + y = 0 ---> (1)

3x - 2y = 10 ---> (2)

Multiplying eq (1) by 2,

2x + 2y = 0 ---> (3)

Adding (2) and (3), we get

5x = 10

x = 2

By applying x = 2 in eq (1),

2 + y = 0

y = -2

Hence, the value of (x, y) is (2, -2).

So, option (B) is correct.

Problem 8 :

2x - 3y = -14

3x - 2y = -6

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

A) -20        B) -8     C) -4      D) 8

Solution:

2x - 3y = -14 ---> (1)

3x - 2y = -6 ---> (2)

(1) × 3 ==> 6x - 9y = -42 ---> (3)

(2) × 2 ==> 6x - 4y = -12 ---> (4)

Subtracting (3) and (4), we get

-5y = -30

y = 6

By applying y = 6 in (1), 

2x - 3(6) = -14

2x - 18 = -14

2x = 4

x = 2

x - y = 2 - 6 = -4

Hence, the value of (x - y) is -4.

So, option (C) is correct.