Answered

IDNLearn.com offers a collaborative platform for sharing and gaining knowledge. Ask your questions and get detailed, reliable answers from our community of experienced experts.

Use the substitution method to solve the following system of equations.

[tex]\[
\begin{cases}
2x - y = 13 \\
4x + 3y = -9
\end{cases}
\][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice:

A. There is one solution. The solution of the system is [tex]\(\square\)[/tex].

(Simplify your answer. Type an ordered pair.)

B. The solution set of the system is [tex]\(\{(x, y) \mid 2x - y = 13\}\)[/tex].

C. The solution set is [tex]\(\varnothing\)[/tex].

Sagot :

GinnyAnsweridn
To solve the system of equations using the substitution method, follow these steps.

Given the system of equations:
[tex]\[ \left\{\begin{array}{l} 2x - y = 13 \\ 4x + 3y = -9 \end{array}\right. \][/tex]

Step 1: Solve one of the equations for one of the variables. Here we can start with the first equation. Let's isolate [tex]\( y \)[/tex]:

[tex]\[ 2x - y = 13 \][/tex]
[tex]\[ -y = 13 - 2x \][/tex]
[tex]\[ y = 2x - 13 \][/tex]

Step 2: Substitute this expression for [tex]\( y \)[/tex] into the second equation:

[tex]\[ 4x + 3(2x - 13) = -9 \][/tex]

Step 3: Simplify and solve for [tex]\( x \)[/tex]:

[tex]\[ 4x + 6x - 39 = -9 \][/tex]
[tex]\[ 10x - 39 = -9 \][/tex]
[tex]\[ 10x = -9 + 39 \][/tex]
[tex]\[ 10x = 30 \][/tex]
[tex]\[ x = 3 \][/tex]

Step 4: Substitute [tex]\( x = 3 \)[/tex] back into the equation we used to express [tex]\( y \)[/tex]:

[tex]\[ y = 2(3) - 13 \][/tex]
[tex]\[ y = 6 - 13 \][/tex]
[tex]\[ y = -7 \][/tex]

So, the solution to the system of equations is:
[tex]\[ (3, -7) \][/tex]

Therefore, the correct choice is:

A. There is one solution. The solution of the system is [tex]\((3, -7)\)[/tex].
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.