Question

Solve this system by substitution: y = 5x - 15 y = 2x - 6 Remember to write your answer as a coordinate point (x,y)

Answer 1

Given the following System of equations:

`\begin{cases}y=5x-15 \\ y=2x-6\end{cases}`

You can use the Substitution method to solve it, as following:

1. Solve for "x" from the first equation:

`\begin{gathered} y=5x-15 \\ y+15=5x \\ \\ x=(y+15)/(5) \end{gathered}`

2. Now you must substitute this equation into the second original equation:

`\begin{gathered} y=2((y+15)/(5))-6 \\ \end{gathered}`

3. Solve for "y":

`\begin{gathered} y=(2y+30)/(5)-6 \\ \\ y+6=(2y+30)/(5) \\ \\ (5)(y+6)=2y+30 \\ 5y+30=2y+30 \\ 3y-2y=30-30 \\ y=0 \end{gathered}`

4. Knowing the value of "y"; you can substitute it into this equation:

`x=(y+15)/(5)`

Then:

`x=((0)+15)/(5)`

5. Evaluating, you get that the value of "x" is:

`\begin{gathered} x=(15)/(5) \\ \\ x=3 \end{gathered}`

Then, the answer is:

`(3,0)`