Question

Using substitution to solve the system below, what expression should be substituted into the first equation? 2x-4y=-4 and x+2y=8

Answer 1

Explanation:

Choices?

Answer 2

Given the system of equation:

`2x-4y=-4` ......[1]

`x+2y=8` ......[2]

we can rewrite equation [2] as;

`x = 8-2y` ......[3]

Substitute equation [3] into [1] to eliminate x, and solve for y;

`2(8-2y)-4y = -4`

Using distributive property:
`a\cdot (b+c) = a\cdot b+ a\cdot c`

`16-4y -4y = -4`

Combine like terms;

16 - 8y = -4

Add 4 to both sides we have;

20 - 8y = 0

Add 8y to both sides we have;

20 = 8y

Divide 8 to both sides we have;

`y = 2.5`

Substitute the y-value in [3] we have;

`x = 8-2(2.5)`

x = 8 - 5 = 3

Therefore, the expression should be substituted into the first equation is,
`x = 8-2y` and also the value of x = 3 and y = 2.5