Question

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

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

ANSWER

$y=12$

EXPLANATION

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

$2x+2=y$

$\Rightarrow 2x=y-2$

$\Rightarrow x=\frac{y}{2}-1--(1)$

The second equation is

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

Let us put equation 1 in 2

$\Rightarrow 2y=5(\frac{y}{2}-1)-1$

$\Rightarrow 2y=\frac{5y}{2}-5-1$

$\Rightarrow 2y=\frac{5y}{2}-6$

Multiplying through by 2 gives;

$\Rightarrow 4y=5y-12$

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

$\Rightarrow -y=-12$

$\Rightarrow y=12$