Question

Use the Substitution Method to solve the following system of equations.
4x + y = 11
x + 2y = 8

Answer 1

do u know how to do it

Answer 2

can you solve the 1st equation for "y"?

Answer 3

yeeah i guess

Answer 4

so, what do you end up?

Answer 5

y=-4x+11

Answer 6

or y = 11-4x... right

Answer 7

yeah

Answer 8

\(\bf 4x + y = 11\\
x + 2y = 8\\
--------------\\
y = 11-4x\\
\textit{now we } \color{blue}{\textit{substitute }} \textit{"y" in the 2nd equation}\\
\textit{since y = 11-4x, then we could say that}\\
x + 2y = 8 \implies x + 2(11-4x) = 8\)

if you were to solve THAT for "x", what would that give you?

Answer 9

-7x+22=8

Answer 10

-7x=-12

Answer 11

8 -22 = -12?

Answer 12

-14

Answer 13

-7x = -14 => x = 2

now that we know that "x = 2"
we can plug it on either equation to find out what "y" is, by solving for "y"

Answer 14

\(\bf 4x + y = 11\\
x + 2y = 8\\
--------------\\
4(2) + y = 11\)

Answer 15

8 + y = 11 => y = 3

Answer 16

let's see if that's the case, x = 2, y = 3
\(\bf 4x + y = 11\\
x + 2y = 8\\
--------------\\
4(2) + 3 = 11\\
2 + 2(3) = 8\)