Respuesta :
Given the following System of equations:
[tex]\begin{cases}y=5x-15 \\ y=2x-6\end{cases}[/tex]You can use the Substitution method to solve it, as following:
1. Solve for "x" from the first equation:
[tex]\begin{gathered} y=5x-15 \\ y+15=5x \\ \\ x=\frac{y+15}{5} \end{gathered}[/tex]2. Now you must substitute this equation into the second original equation:
[tex]\begin{gathered} y=2(\frac{y+15}{5})-6 \\ \end{gathered}[/tex]3. Solve for "y":
[tex]\begin{gathered} y=\frac{2y+30}{5}-6 \\ \\ y+6=\frac{2y+30}{5} \\ \\ (5)(y+6)=2y+30 \\ 5y+30=2y+30 \\ 3y-2y=30-30 \\ y=0 \end{gathered}[/tex]4. Knowing the value of "y"; you can substitute it into this equation:
[tex]x=\frac{y+15}{5}[/tex]Then:
[tex]x=\frac{(0)+15}{5}[/tex]5. Evaluating, you get that the value of "x" is:
[tex]\begin{gathered} x=\frac{15}{5} \\ \\ x=3 \end{gathered}[/tex]Then, the answer is:
[tex](3,0)[/tex]