System of equations, solve by substitution? 3x + 2y = -10 and 5x - y = -8??

Question

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Answer 1

Substitution method

Given equations are 3x+2y = -10 ---------> (1)

5x-y = -8

Add y to each side.

5x-y+y = -8+y

5x = -8+y

Divide to each side by 5.

5x/5 = (-8+y)/5

x = (-8+y)/5

Substitute the x value in (1).

3(-8+y)/5+2y = -10

(-24+3y)/5+2y = -10

-24/5+3y/5+2y = -10

(3y+10y)/5 = -10+24/5

13y/5 = (-50+24)/5

Multiple to each side by 5.

5(13y)/5 = 5(-50+24)/5

13y = -26

divide to each side by 13.

13y/13 = -26/13

⇒ y = -2

Substitute the y value in (1).

3x+2*-2 = -10

3x-4 = -10

subtract 4 from each side.

3x+4-4 = -10+4

3x = -6

Divide to each side by 3.

3x/3 = -6/3

⇒ x = -2

Solution x = -2, y =-2.