Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
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]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.