Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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 using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.