Question

Solve this system of equations. 3x + 4y = 36 1 8 3*+8 y=

Answer 1

x = 96488−(4y/3)

Isolate the variable by dividing each side by factors that don't contain the variable.

y = 72366−(3x/4)

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer 2

x=4, y=6 or ( 4,6)

1) Let's solve this by making use of the Substitution Method

3x+ 4y = 36

y= -1/2x+8

2) Plugging into the first one the 2nd equation:

`\begin{gathered} 3x+4(-(1)/(2)x+8)=36 \\ 3x\text{ -2x+32=36} \\ x+32=36 \\ x=36-32 \\ x=4 \end{gathered}`

Note that we combined like terms on the 2nd line

And subtracted 32 from both sides.

2.2) Now we can plug into any of them, x=4

`\begin{gathered} y=-(1)/(2)(4)+8 \\ y=-2+8 \\ y=6 \end{gathered}`

2.3) Testing those solutions we can write out:

`\begin{gathered} (4,6) \\ 6=-(1)/(2)(4)+8 \\ 6=-2+8 \\ 6=6\text{ TRUE} \\ 3x+4y=36 \\ 3(4)+4(6_{})=36 \\ 12+24=36 \\ 36=36\text{ TRUE} \end{gathered}`

3) Hence, we can state that the answer is x=4, y=6