Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Solve using any method you choose:

[tex]\[ 4x + y = 8 \][/tex]
[tex]\[ -3x - y = 0 \][/tex]

A. [tex]\((-8, -24)\)[/tex]
B. [tex]\((8, -24)\)[/tex]
C. [tex]\((-8, 24)\)[/tex]
D. [tex]\((8, 24)\)[/tex]

Sagot :

GinnyAnswer
To solve the system of linear equations:
[tex]\[ 4x + y = 8 \][/tex]
[tex]\[ -3x - y = 0 \][/tex]

Let us solve it step-by-step.

First, we'll add the two equations together to eliminate [tex]\( y \)[/tex]. This can be done directly since the coefficients of [tex]\( y \)[/tex] in both equations are opposites ([tex]\(+ y\)[/tex] and [tex]\( - y \)[/tex]):

[tex]\[ (4x + y) + (-3x - y) = 8 + 0 \][/tex]

Simplify:
[tex]\[ 4x - 3x + y - y = 8 \][/tex]
[tex]\[ x = 8 \][/tex]

Now that we have [tex]\( x = 8 \)[/tex], substitute this value back into one of the original equations to solve for [tex]\( y \)[/tex]. We’ll use the first equation:

[tex]\[ 4x + y = 8 \][/tex]

Substitute [tex]\( x = 8 \)[/tex]:
[tex]\[ 4(8) + y = 8 \][/tex]
[tex]\[ 32 + y = 8 \][/tex]

Solve for [tex]\( y \)[/tex]:
[tex]\[ y = 8 - 32 \][/tex]
[tex]\[ y = -24 \][/tex]

Thus, the solution to the system of equations is:
[tex]\[ x = 8 \][/tex]
[tex]\[ y = -24 \][/tex]

Therefore, the correct answer is [tex]\( (8, -24) \)[/tex].
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.