Question

SOLVE THE SYSTEM3x+y=25x+2y=5

Answer 1

Use the substitution method to solve the system of equations.

Notice that the coefficient of y in the first equation is 1:

`3x+y=2`

Then, isolate y from the first equation. Next, replace the expression for y in the second equation to obtain a single equation with the x-variable only:

`\begin{gathered} 3x+y=2 \\ \Rightarrow y=2-3x \end{gathered}`
`\begin{gathered} 5x+2y=5 \\ \Rightarrow5x+2(2-3x)=5 \end{gathered}`

Solve for x:

`\begin{gathered} \Rightarrow5x+4-6x=5 \\ \Rightarrow-x+4=5 \\ \Rightarrow-x=5-4 \\ \Rightarrow-x=1 \\ \\ \therefore x=-1 \end{gathered}`

Replace the value of x into the expression for y:

`\begin{gathered} y=2-3x \\ \Rightarrow y=2-3(-1) \\ \Rightarrow y=2+3 \\ \\ \therefore y=5 \end{gathered}`

Therefore, the solution for the given system of equations is:

`\begin{gathered} x=-1 \\ y=5 \end{gathered}`