Respuesta :

So,

We're going to solve the system:

[tex]\begin{cases}y=5x+7 \\ y=3x+1\end{cases}[/tex]

Using substitution.

What we're going to do, is to replace the expression for y in the second equation so we sould state a linear equation with only one variable:

[tex]y=3x+1\text{ }(\leftrightarrow)\text{ }5x+7=3x+1[/tex]

Now, let's solve this equation for x:

[tex]\begin{gathered} 5x+7=3x+1 \\ 5x-3x=1-7 \\ 2x=-6 \\ x=-3 \end{gathered}[/tex]

To find the value of y, we just replace the value of x in any of both equations:

[tex]\begin{gathered} y=3x+1 \\ y=3(-3)+1 \\ y=-8 \end{gathered}[/tex]

Then, the solution of the system is:

[tex](x,y)=(-3,-8)[/tex]

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