Question

Solve the system of equations below.x + y = 83x + 2y = 21 (3, 5) (5, 3) (2, 6) (6, 2)

Answer 1

We have the following system of equations:

$\begin{cases}x+y={8} \\ 3x+2y={21}\end{cases}$

To solve that equation we can do a simple substitution

$\begin{gathered} x+y=8 \\ \\ y=8-x \end{gathered}$

Then

$\begin{gathered} 3x+2y=21 \\ \\ 3x+2(8-x)=21 \end{gathered}$

And solve the equation for x

$\begin{gathered} 3x+16-2x=21 \\ \\ x=21-16 \\ \\ x=5 \end{gathered}$

Now we have the value of x, we can find the value of y

$\begin{gathered} y=8-x \\ \\ y=8-5 \\ \\ y=3 \end{gathered}$

The solution is

$(5,3)$