Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
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]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.