We are given the following system of equations:
[tex]\begin{gathered} x=2y,(1) \\ 4y=300-x,(2) \end{gathered}[/tex]
In order to use the method of substitution we will multiply equation (1) by 2;
[tex]2x=4y[/tex]
Now we replace this value in equation (2):
[tex]2x=300-x[/tex]
Now we solve for "x" first by adding "x" to both sides:
[tex]\begin{gathered} 2x+x=300-x+x \\ 3x=300 \end{gathered}[/tex]
Now we divide both sides by 3:
[tex]x=\frac{300}{3}=100[/tex]
Now we substitute this value in equation (1):
[tex]100=2y[/tex]
dividing both sides by 2:
[tex]\begin{gathered} \frac{100}{2}=y \\ 50=y \end{gathered}[/tex]
Therefore, the solution is:
[tex](100,50)[/tex]
