Question

Solve the following system: 3x + 3y = 42 x – 3y = –22 a) No Solution b) Infinite Solutions c) (-5,-9) d) (5,9)

Answer 1

We are given the following system of equations:

$\begin{gathered} 3x+3y=42,\text{ (1)} \\ x-3y=-22\text{, (2)} \end{gathered}$

Equation (1) can be rewritten by dividing by 3 on both sides as:

$x+y=14,\text{ (1)}$

Solving for "x" in equation (1), we get:

$x=14-y$

Replacing in equation (2)

$\begin{gathered} x-3y=-22 \\ 14-y-3y=-22 \end{gathered}$

simplifying

$14-4y=-22$

Now we solve for "y", by subtracting 14 on both sides:

$\begin{gathered} 14-14-4y=-22-14 \\ -4y=-36 \end{gathered}$

Dividing by -4 on both sides:

$y=-\frac{36}{-4}=9$

Replacing the value of "y" in equation (1)

$\begin{gathered} x+y=14 \\ x+9=14 \end{gathered}$

Now we subtract 9 on both sides:

$\begin{gathered} x+9-9=14-9 \\ x=5 \end{gathered}$

Therefore, the solution of the system is:

$(x,y)=(5,9)$