Answer:
[tex](2,1)[/tex].
Step-by-step explanation:
We have been given a system of equations. We are asked to solve our given system using elimination method.
[tex]-3y=x-5...(1)[/tex]
[tex]x+5y=7...(2)[/tex]
First of all, we will gather all terms of both equations on left side as shown below:
[tex]-x-3y+5=0...(1)[/tex]
[tex]x+5y-7=0...(2)[/tex]
Adding equation (1) and (2), we will get:
[tex]-x+x-3y+5y+5-7=0\rightarrow 2y-2=0[/tex]
Now, we will add 2 on both sides of our equation as shown below:
[tex]2y-2+2=0+2[/tex]
[tex]2y=2[/tex]
[tex]\frac{2y}{2}=\frac{2}{2}[/tex]
[tex]y=1[/tex]
Upon substituting [tex]y=1[/tex] in equation (2), we will get:
[tex]x+5*1=7[/tex]
[tex]x+5=7[/tex]
[tex]x=7-5[/tex]
[tex]x=2[/tex]
Therefore, the solution for our given system of equations would be [tex](2,1)[/tex].
