Answer:
[tex]\boxed {\boxed {\sf (5, -4)}}[/tex]
Step-by-step explanation:
We are given the two equations:
[tex]y= -2x+6 \\-4x-6y=4[/tex]
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.
[tex]-4x-6y=4[/tex]
[tex]-4x-6(-2x+6)=4[/tex]
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.
[tex]-4x+ (-6*-2x)+(-6*6)=4[/tex]
[tex]-4x+12x+(-6*6)=4[/tex]
[tex]-4x+12x-36=4[/tex]
Combine like terms. There are 2 x terms that can be added.
[tex](-4x+12x)-36=4[/tex]
[tex]8x-36=4[/tex]
36 is being subtracted from 8x. The inverse of subtraction is addition, so add 36 to both sides of the equation.
[tex]8x-36+36=4+36[/tex]
[tex]8x=40[/tex]
x is being multiplied by 8. The inverse of multiplication is division, so divide both sides by 8.
[tex]\frac{8x}{8} =\frac{40}{8}[/tex]
[tex]x=5[/tex]
x is known, so we can find y using the first equation.
[tex]y=-2x+6[/tex]
x is equal to 5, so substitute the value in.
[tex]y=-2(5)+6[/tex]
Multiply first.
[tex]y=-10+6[/tex]
Add.
[tex]y=-4[/tex]
A solution is written as (x,y). So, the solution to this equation is (5, -4).
