Respuesta :
Given the system of equations:
4x + y = 7
x = 3y - 8
Let's solve using the substitution method.
To solve using substitution method, apply the following steps:
Step 1:
Substitute (3y - 8) for x in equation 1
[tex]\begin{gathered} 4x+y=7 \\ \\ 4(3y-8)+y=7 \end{gathered}[/tex]Step 2:
Apply distributive property:
[tex]\begin{gathered} 4(3y)+4(-8)+y=7 \\ \\ 12y-32+y=7 \end{gathered}[/tex]Combine like terms:
[tex]\begin{gathered} 13y+y-32=7 \\ \\ 13y-32=7 \end{gathered}[/tex]Step 3.
Solve for y.
Add 32 to both sides:
[tex]\begin{gathered} 13y-32+32=7+32 \\ \\ 13y=39 \\ \\ \text{ Divide both sides by 13:} \\ \frac{13y}{13}=\frac{39}{13} \\ \\ y=3 \end{gathered}[/tex]Step 4.
Substitute 3 for y in either of the equations.
Take equation 2:
[tex]\begin{gathered} x=3y-8 \\ \\ x=3(3)-8 \\ \\ x=9-8 \\ \\ x=1 \end{gathered}[/tex]Therefore, we have the solution:
x = 1, y = 3
ANSWER:
• x = 1
,• y = 3
