Answer :
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 { \ }
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 { \ }
