Question

Solve using the substitution method 4x+y=7x=3y-8

Answer 1

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

`\begin{gathered} 4x+y=7 \\ \\ 4(3y-8)+y=7 \end{gathered}`

Step 2:

Apply distributive property:

`\begin{gathered} 4(3y)+4(-8)+y=7 \\ \\ 12y-32+y=7 \end{gathered}`

Combine like terms:

`\begin{gathered} 13y+y-32=7 \\ \\ 13y-32=7 \end{gathered}`

Step 3.

Solve for y.

Add 32 to both sides:

`\begin{gathered} 13y-32+32=7+32 \\ \\ 13y=39 \\ \\ \text{ Divide both sides by 13:} \\ (13y)/(13)=(39)/(13) \\ \\ y=3 \end{gathered}`

Step 4.

Substitute 3 for y in either of the equations.

Take equation 2:

`\begin{gathered} x=3y-8 \\ \\ x=3(3)-8 \\ \\ x=9-8 \\ \\ x=1 \end{gathered}`

Therefore, we have the solution:

x = 1, y = 3

ANSWER:

• x = 1

,

• y = 3