Set two equations equal to each other

Hello, odumath!

We have a system of equation to solve: \(\displaystyle \L\begin{array}{cc}x\,+\,2y & = &40 \\4x\,+\,3y & = & 120\end{array}\)

To solve it, we will eliminate one of the variables (legally).

Multiply the first equation by -4:    −4x − 8y = −160\displaystyle 4:\;\;-4x\,-\,8y\:=\:-160
. . . . .Add the second equation:      4x + 3y =    120\displaystyle \;\;\:4x\,+\,3y\:=\;\;120

And we get:  −5y = −40    ⇒    y = 8\displaystyle \:-5y\:=\:-40\;\;\Rightarrow\;\;\fbox{y\:=\:8}

Substitute into the first equation:  x + 2(8) = 40    ⇒    x = 24\displaystyle \:x\,+\,2(8)\:=\:40\;\;\Rightarrow\;\;\fbox{x\:=\:24}


And there are the solutions:  x = 24, y = 8\displaystyle \:x\,=\,24,\:y\,=\,8

 
Thanks... your solution is easy to follow.

I appreciate your help!

odumath
 
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