Assignment

Using Substitution to Solve an Equation with Two Variables

What is the value of [tex]$x$[/tex] in the equation [tex]$3x - 4y = 65$[/tex] when [tex][tex]$y = 4$[/tex][/tex]?

A. [tex]$x = 13 \frac{1}{4}$[/tex]
B. [tex]$x = 21 \frac{2}{3}$[/tex]
C. [tex][tex]$x = 23$[/tex][/tex]
D. [tex]$x = 27$[/tex]



Answer :

To determine the value of [tex]\( x \)[/tex] in the equation [tex]\( 3x - 4y = 65 \)[/tex] given [tex]\( y = 4 \)[/tex], let's follow these steps:

1. Substitute [tex]\( y = 4 \)[/tex] into the equation:

The given equation is:
[tex]\[ 3x - 4y = 65 \][/tex]

2. Replace [tex]\( y \)[/tex] with 4:
[tex]\[ 3x - 4(4) = 65 \][/tex]

3. Simplify the equation:
[tex]\[ 3x - 16 = 65 \][/tex]

4. Isolate the term with [tex]\( x \)[/tex]:
Add 16 to both sides of the equation:
[tex]\[ 3x - 16 + 16 = 65 + 16 \][/tex]
[tex]\[ 3x = 81 \][/tex]

5. Solve for [tex]\( x \)[/tex]:
Divide both sides by 3:
[tex]\[ x = \frac{81}{3} \][/tex]
[tex]\[ x = 27 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex] is [tex]\( \boxed{27} \)[/tex].