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.

 From (1), 3y = kx - 4y = (k/3) x - (4/3) From (2), 5y = 4x - 7y = (4/5) x - (7/5)

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.

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