Question

In the following exercises, solve the systems of equations by substitution.
$$\begin{gathered} 5x-2y=-6 \\ y=3x+3 \end{gathered}$$

Short answer

The solution set is $(0,3)$.

Step-by-step solution

Step 1. Given Information

In the following exercises, we have to solve the systems of equations by substitution.
$$\begin{gathered} 5x-2y=-6 \\ y=3x+3 \end{gathered}$$

Step 2. Putting the value of y from the second equation in the first equation .

$$\begin{gathered} 5x-2(3x+3)=-6 \\ 5x-6x-6=-6 \\ -x-6=-6 \\ Add6onbothside \\ -x-6+6=-6+6 \\ -x=0 \\ x=0 \end{gathered}$$

Step 3. Putting the value of x in the equation y=3x+3.

$$\begin{gathered} y=3\times 0+3 \\ y=0+3 \\ y=3 \end{gathered}$$