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 -\(\displaystyle 4:\;\;-4x\,-\,8y\:=\:-160\)
. . . . .Add the second equation: \(\displaystyle \;\;\:4x\,+\,3y\:=\;\;120\)

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

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


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

 
Thanks... your solution is easy to follow.

I appreciate your help!

odumath
 
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