Tatiana7121idn
Answered

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Which of these shows the result of using the first equation to substitute for [tex]y[/tex] in the second equation, then combining like terms?

[tex]\[
\begin{array}{l}
y = 3x \\
2x + 3y = 55
\end{array}
\][/tex]

A. [tex]5x = 55[/tex]

B. [tex]11x = 55[/tex]

C. [tex]9x = 55[/tex]

D. [tex]5y = 55[/tex]

Sagot :

GinnyAnsweridn
To solve this system of equations step-by-step, we start with the given equations:

[tex]\[ \begin{array}{l} y = 3x \\ 2x + 3y = 55 \\ \end{array} \][/tex]

We need to substitute the expression for [tex]\( y \)[/tex] from the first equation into the second equation.

1. From the first equation [tex]\( y = 3x \)[/tex], substitute [tex]\( 3x \)[/tex] for [tex]\( y \)[/tex] in the second equation:

[tex]\[ 2x + 3(3x) = 55 \][/tex]

2. Now simplify the equation by combining like terms:

[tex]\[ 2x + 9x = 55 \][/tex]

3. Combine the like terms on the left side:

[tex]\[ 11x = 55 \][/tex]

So, the result of substituting the first equation into the second equation and combining like terms is:

[tex]\[ 11x = 55 \][/tex]

Thus, the correct answer is:

B. [tex]\( 11x = 55 \)[/tex]
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