Question

Solve the system of linear equations below by substitution.

Answer 1

Answer:

(5, -4)

Step-by-step 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

Answer:

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

Step-by-step 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.

$\frac{8x}{8} =\frac{40}{8}$

$x=5$

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).