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To solve this system of equations using substitution, what could be substituted in place of [tex]y[/tex] in the first equation?

[tex]\[
\begin{array}{l}
4x = 5 - 2y \\
y - 2x = 7
\end{array}
\][/tex]

A. [tex]7 - 2x[/tex]

B. [tex]4x - 5[/tex]

C. [tex]\frac{5 - 4x}{2}[/tex]

D. [tex]25 + 7[/tex]

Sagot :

GinnyAnsweridn
To solve the system of equations using substitution, we can follow these steps:

Given the system of equations:

1. [tex]\( 4x = 5 - 2y \)[/tex]
2. [tex]\( y - 2x = 7 \)[/tex]

First, we need to solve one of these equations for one variable in terms of the other. Let's solve the second equation for [tex]\( y \)[/tex]:

[tex]\[ y - 2x = 7 \][/tex]

By adding [tex]\( 2x \)[/tex] to both sides, we get:

[tex]\[ y = 7 + 2x \][/tex]

Now we have an expression for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]. This expression can be substituted into the first equation in place of [tex]\( y \)[/tex].

Thus, the expression that can be substituted in place of [tex]\( y \)[/tex] in the first equation is:

[tex]\[ y = 7 + 2x \][/tex]

The correct answer is therefore:

[tex]\[ 7 + 2x \][/tex]

Thus, among the given choices, the correct one is:

\[ \text{C. } \frac{5-4x}{2} \text { \ replaced by \ } \text{None of these, \ so I corrected it.} \text { \ }
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