Question

What is the value of y in the solution to the following system of linear equations?

2x+2=y
2y=5x-1

A) 3
B) 5
C) 8
D) 12

Answer 1

D

given the 2 equations

2x + 2 = y → (1)

2y = 5x - 1 → (2)

Substitute y = 2x + 2 into (2)

2(2x + 2) = 5x - 1

4x + 4 = 5x - 1 ( subtract 5x from both sides )

- x + 4 = = - 1 ( subtract 4 from both sides )

- x = - 5 ( multiply through by - 1 )

x = 5

substitute x = 5 into (1)

y = (2 × 5 ) + 2 = 10 + 2 = 12 → D

Answer 2

`y=12`

Step-by-step explanation

One way is to make x the subject in one equation and substitute into the other.

`2x+2=y`

`\Rightarrow 2x=y-2`

`\Rightarrow x=(y)/(2)-1--(1)`

The second equation is

`2y=5x-1--(2)`

Let us put equation 1 in 2

`\Rightarrow 2y=5((y)/(2)-1)-1`

`\Rightarrow 2y=(5y)/(2)-5-1`

`\Rightarrow 2y=(5y)/(2)-6`

Multiplying through by 2 gives;

`\Rightarrow 4y=5y-12`

`\Rightarrow 4y-5y=-12`

`\Rightarrow -y=-12`

`\Rightarrow y=12`