Question

Solve the system of linear equations below by substitution.

y = -2x + 6

-4x - 6y = 4

Group of answer choices

(-2, 10)

(5, -4)

(3, 0)

(0, 6)

Answer 1

(5, -4)

Explanation:

Substitute y from the first equation into the second equation:

-4x - 6(-2x + 6) = 4

Simplify:

-4x + 12x - 36 = 4

8x = 40

x = 5

The only answer choice where x = 5 is (5, -4).

Answer 2

`\boxed {\boxed {\sf (5, -4)}}`

Explanation:

We are given the two equations:

`y= -2x+6 \\-4x-6y=4`

We are asked to solve by substitution. Since we know that y is equal to -2x+6, so we can substitute the expression in for y in the second equation.

`-4x-6y=4`

`-4x-6(-2x+6)=4`

Now, solve for x by isolating the variable on one side of the equation.

First, distribute the -6 into the expression. Multiply each term in the parentheses by -6.

`-4x+ (-6*-2x)+(-6*6)=4`

`-4x+12x+(-6*6)=4`

`-4x+12x-36=4`

Combine like terms. There are 2 x terms that can be added.

`(-4x+12x)-36=4`

`8x-36=4`

36 is being subtracted from 8x. The inverse of subtraction is addition, so add 36 to both sides of the equation.

`8x-36+36=4+36`

`8x=40`

x is being multiplied by 8. The inverse of multiplication is division, so divide both sides by 8.

`(8x)/(8) =(40)/(8)`

`x=5`

x is known, so we can find y using the first equation.

`y=-2x+6`

x is equal to 5, so substitute the value in.

`y=-2(5)+6`

Multiply first.

`y=-10+6`

Add.

`y=-4`

A solution is written as (x,y). So, the solution to this equation is (5, -4).