904jasmineidn
Answered

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If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the first equation is substituted into the second equation:

[tex]\[
\begin{array}{l}
6x - y = 1 \\
4x - 3y = -11
\end{array}
\][/tex]

A. [tex]\(4(-6x + 1) - 3y = -11\)[/tex]

B. [tex]\(4(6x + 1) - 3y = -11\)[/tex]

C. [tex]\(4x - 3(6x - 1) = -11\)[/tex]

D. [tex]\(4x - 3(-6x - 1) = -11\)[/tex]

Sagot :

GinnyAnsweridn
Let's solve the system of equations step-by-step using the substitution method.

The given system of equations is:

[tex]\[ \begin{array}{l} 6x - y = 1 \quad \text{(1)} \\ 4x - 3y = -11 \quad \text{(2)} \end{array} \][/tex]

1. Solve the first equation for [tex]\(y\)[/tex]:

[tex]\[ 6x - y = 1 \][/tex]
[tex]\[ -y = 1 - 6x \][/tex]
[tex]\[ y = 6x - 1 \][/tex]

2. Substitute [tex]\(y = 6x - 1\)[/tex] into the second equation (Equation 2):

[tex]\[ 4x - 3(6x - 1) = -11 \][/tex]

Now let's verify which of the given choices corresponds to this substitution. Simplify the above equation step by step:

[tex]\[ 4x - 3(6x - 1) = -11 \][/tex]
[tex]\[ 4x - 18x + 3 = -11 \][/tex]

Simplify further if necessary, but at this step, the new equation after substituting [tex]\(y\)[/tex] from the first equation into the second equation clearly matches:

[tex]\[ 4x - 3(6x - 1) = -11 \][/tex]

So, the correct choice is:

[tex]\[ 4x - 3(6x - 1) = -11 \][/tex]

Therefore, the answer is indeed [tex]\(\boxed{4 x-3(6 x-1)=-11}\)[/tex].
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