Answer:
(14, -2)
Step-by-step explanation:
To solve by using substitution, begin by solving for a variable in the first equation. Let's solve for x:
[tex]x+8y=-2\\x=-2-8y[/tex]
Now we know what x equals. Let's substitute this into the second equation:
[tex]x-3y=20\\(-2-8y)-3y=20[/tex]
We can then simplify:
[tex]-2-8y-3y=20[/tex] Given equation
[tex]-2-11y=20[/tex] Combine y terms
[tex]-11y=22[/tex] Add 2
[tex]y=-2[/tex] Divide by -11
So, we now know the value of y = -2.
To find the value of X, we can substitute the value of Y into one of the equations. Let's use the first one:
[tex]x+8y=-2[/tex]
[tex]x+8(-2)=-2[/tex] Substitute for y
[tex]x-16=-2[/tex] Distribute 8
[tex]x=14[/tex] Add 16
So, we now know the value of x = 14.
Therefore, we know a solution to the system of equations is (14, -2).
