Question

Solve the following system of equations using Substitution, showing all work.
`y = 2x + 3 \\ 2x + 5y = 3`

Answer 1

We're going to solve the system of equations:

`\begin{cases}y=2x+3 \\ 2x+5y=3\end{cases}`

Using substitution.

For this, all we need to do is to replace the first equation in the second one:

`\begin{gathered} 2x+5y=3 \\ Given\text{ }y=2x+3\colon \\ 2x+5(2x+3)=3 \end{gathered}`

Now, we could solve this linear equation:

`\begin{gathered} 2x+5(2x+3)=3 \\ 2x+10x+15=3 \\ 12x+15=3 \\ 12x=-12 \\ x=-1 \end{gathered}`

Therefore, x=-1.

Now, to find the value of y we could replace x=-1 in any of both equations:

`\begin{gathered} y=2x+3 \\ y=2(-1)+3 \\ y=-2+3 \\ y=1 \end{gathered}`

Therefore, x = -1 , y = 1, and the solution of the system is (x,y)=(-1,1).