Question

Solve using substitution. y = 5x + 7y = 3x + 1

Answer 1

So,

We're going to solve the system:

`\begin{cases}y=5x+7 \\ y=3x+1\end{cases}`

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:

`y=3x+1\text{ }(\leftrightarrow)\text{ }5x+7=3x+1`

Now, let's solve this equation for x:

`\begin{gathered} 5x+7=3x+1 \\ 5x-3x=1-7 \\ 2x=-6 \\ x=-3 \end{gathered}`

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

`\begin{gathered} y=3x+1 \\ y=3(-3)+1 \\ y=-8 \end{gathered}`

Then, the solution of the system is:

`(x,y)=(-3,-8)`