Respuesta :
To solve the system of equations by the substitution method, choose any variables and solve for any equations.
[tex]\begin{cases}y=2x-7\Rightarrow\text{ Equation 1} \\ 4x+y=17\Rightarrow\text{ Equation 2}\end{cases}[/tex]As you can see in Equation 1, the variable y is already solved:
[tex]y=2x-7\Rightarrow\text{ Equation 1}[/tex]Now, substitute the value of y in Equation 2:
[tex]\begin{gathered} 4x+y=17\Rightarrow\text{ Equation 2} \\ 4x+2x-7=17 \end{gathered}[/tex]Now, we can solve the above equation for x:
[tex]\begin{gathered} 4x+2x-7=17 \\ \text{ Add similar terms to the left side of the equation} \\ 6x-7=17 \\ \text{ Add 7 from both sides of the equation} \\ 6x-7+7=17+7 \\ 6x=24 \\ \text{ Divide by 6 from both sides of the equation} \\ \frac{6x}{6}=\frac{24}{6} \\ \boldsymbol{x=4} \end{gathered}[/tex]Finally, we replace the value of x in any of the initial equations, for example, in Equation 1:
[tex]\begin{gathered} y=2x-7\Rightarrow\text{ Equation 1} \\ y=2\cdot4-7 \\ y=8-7 \\ \boldsymbol{y=1} \end{gathered}[/tex]Therefore, the solution of the given system of equations is
[tex]\begin{cases}\boldsymbol{x=4} \\ \boldsymbol{y=1}\end{cases}[/tex]