Raj tried to solve the system below.

9x-y=15

2x+8y=28

Raj's Work

9x - y = 15 2x + 8y (15 + 9x) = 28 9 (-46/37) - y = 15

-y = 15 - 9x 2x + 120 + 72x = 28 - 414/37 - y = 15

y = - 15 + 9x 74x + 120 = 28 y = 969/37

74x = - 92

x = - 46/37

What error did Raj make?

A) Rag forgot to multiply the value of x by 9 when solving for the value of y.

B) When Raj solved for the value of x, he subtracted 120 from both sides.

C) Raj forgot the negative when substituting - 15 + 9x for y.

D) Raj found the value of - y instead of y.

Answer: Option C) Raj forgot the negative when substituting - 15+9x for y.

Solution:

(1) 9x-y=15

(2) 2x+8y=28

Isolating y in the first equation. Subtracting 9x both sides of the equation:

(1) 9x-y-9x=15-9x

Subtracting:

(1) - y=15-9x

Multiplying both sides of the equation by - 1:

(1) (-1) (-y) = (-1) (15-9x)

(1) y=-15+9x

Then Raj found the value of y. It's not option D.

Substitutng y by - 15+9x in the second equation:

(2) 2x+8 (-15+9x) = 28

Then option C) is the answer: Raj forgot the negative when substituting - 15+9x for y.

Eliminating the parentheses applying the distributive property in the multiplication:

(2) 2x-120+72x=28

Adding similar terms:

(2) 74x-120=28

Solving for x. Adding 120 both sides of the equation:

(2) 74x-120+120=28+120

Adding:

(2) 74x=148

Dividing both sides of the equation by 74:

(2) 74x/74=148/74

Dividing:

(2) x=2

Solving for y: Replacing x by 2 in the first equation:

(1) y=-15+9x

(1) y=-15+9 (2)

Multiplying:

(1) y=-15+18

Subtracting:

(1) y=3