Answer:
Our system of equations is:
[tex]\begin{cases}4x+5y={1} \\ y={2x+3}\end{cases}[/tex]And its solution is:
[tex]\begin{gathered} x=-1 \\ y=1 \end{gathered}[/tex]Step-by-step explanation:
First, we'll fill out the second equation.
We'll choose a value for x. In this case, we'll work with:
[tex]x=-1[/tex]Now, we'll chose 2 as a coefficient for x and 3 as the independent term. This way, we'll have the equation:
[tex]y=2x+3[/tex]And since we've established that x = 1,
[tex]\begin{gathered} y=2(-1)+3 \\ \rightarrow y=1 \end{gathered}[/tex]From now on, we know that the solution to our system is:
[tex]\begin{gathered} x=-1 \\ y=1 \end{gathered}[/tex]Now, we'll work on the first equation. We'll chose 4 as a coefficient for x and 5 as a coefficient for y. This way, we'll have the expression:
[tex]4x+5y[/tex]And since we already know the values of x and y, we'll have that:
[tex]4x+5y\rightarrow4(-1)+5(1)\rightarrow1[/tex]Therefore, our first equation is:
[tex]4x+5y=1[/tex]Therefore, we can conclude that our system of equations is:
[tex]\begin{cases}4x+5y={1} \\ y={2x+3}\end{cases}[/tex]And its solution is:
[tex]\begin{gathered} x=-1 \\ y=1 \end{gathered}[/tex]