Question

Solve the system using elimination.

2x – 2y = –8
x + 2y = –1

(–3, 1)

(–14, 1)

(0, 4)

(1, 5)

Answer 1

(–3, 1)

Explanation:

Step 1: Solve for x

2x – 2y = –8 -----------(1)

x + 2y = –1. -------------(2)

• Add equation 1 to 2

⇒2x + x| -2y + 2y |= -8 -1

⇒3x = -9

• Divide both side by the coefficient of x

⇒3x/3 = -9/3

⇒x = -3

Step 2; Solve for y

• Substitute into equation 2

x + 2y = –1

(-3) + 2y = -1

• Add 3 from both sides

-3 + 2y + 3 = -1 + 3

2y = 2

• divide both side by two

2y/2 = 2/2

y = 1

So, ( x,y) ⇒(-3,1)

Answer 2

(- 3, 1 )

Explanation:

2x - 2y = - 8 → (1)

x + 2y = - 1 → (2)

adding the 2 equations term by term will eliminate y

3x + 0 = - 9

3x = - 9 ( divide both sides by 3 )

x = - 3

substitute x = - 3 into either of the 2 equations and solve for y

substituting into (2)

- 3 + 2y = - 1 ( add 3 to both sides )

2y = 2 ( divide both sides by 2 )

y = 1

solution is (- 3, 1 )