Answer :
Certainly! To solve the system of linear equations using the substitution method, we have the following equations:
[tex]\[ \begin{array}{l} y = 4x \\ y = 8x + 8 \end{array} \][/tex]
1. Step 1: Substitute the value of \( y \) from the first equation into the second equation.
Given \( y = 4x \), we can replace \( y \) in the second equation \( y = 8x + 8 \).
So, substituting \( y \) in the second equation, we get:
[tex]\[ 4x = 8x + 8 \][/tex]
2. Step 2: Solve for \( x \).
Rearrange the equation to move all terms involving \( x \) to one side:
[tex]\[ 4x - 8x = 8 \][/tex]
Simplify the left-hand side:
[tex]\[ -4x = 8 \][/tex]
Divide both sides by \(-4\) to solve for \( x \):
[tex]\[ x = -2 \][/tex]
3. Step 3: Substitute \( x \) back into the first equation to find \( y \).
Now, substitute \( x = -2 \) back into the first equation \( y = 4x \):
[tex]\[ y = 4(-2) \][/tex]
Simplify to find \( y \):
[tex]\[ y = -8 \][/tex]
So, the solution to the system of equations is:
[tex]\[ (x, y) = (-2, -8) \][/tex]
To confirm, the correct solution from the given options is:
[tex]\[ (-2, -8) \][/tex]
[tex]\[ \begin{array}{l} y = 4x \\ y = 8x + 8 \end{array} \][/tex]
1. Step 1: Substitute the value of \( y \) from the first equation into the second equation.
Given \( y = 4x \), we can replace \( y \) in the second equation \( y = 8x + 8 \).
So, substituting \( y \) in the second equation, we get:
[tex]\[ 4x = 8x + 8 \][/tex]
2. Step 2: Solve for \( x \).
Rearrange the equation to move all terms involving \( x \) to one side:
[tex]\[ 4x - 8x = 8 \][/tex]
Simplify the left-hand side:
[tex]\[ -4x = 8 \][/tex]
Divide both sides by \(-4\) to solve for \( x \):
[tex]\[ x = -2 \][/tex]
3. Step 3: Substitute \( x \) back into the first equation to find \( y \).
Now, substitute \( x = -2 \) back into the first equation \( y = 4x \):
[tex]\[ y = 4(-2) \][/tex]
Simplify to find \( y \):
[tex]\[ y = -8 \][/tex]
So, the solution to the system of equations is:
[tex]\[ (x, y) = (-2, -8) \][/tex]
To confirm, the correct solution from the given options is:
[tex]\[ (-2, -8) \][/tex]
