To solve the system of equations using substitution, we will go through the following steps:
1. Identify the equations:
[tex]\[
x = 2y
\][/tex]
[tex]\[
4y = 300 - x
\][/tex]
2. Substitute the value of [tex]\( x \)[/tex] from the first equation into the second equation:
Since [tex]\( x = 2y \)[/tex], substitute [tex]\( 2y \)[/tex] for [tex]\( x \)[/tex] in the second equation:
[tex]\[
4y = 300 - 2y
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
Add [tex]\( 2y \)[/tex] to both sides to combine the [tex]\( y \)[/tex] terms:
[tex]\[
4y + 2y = 300
\][/tex]
Simplify by combining like terms:
[tex]\[
6y = 300
\][/tex]
Divide both sides by 6 to isolate [tex]\( y \)[/tex]:
[tex]\[
y = \frac{300}{6}
\][/tex]
Simplify the division:
[tex]\[
y = 50
\][/tex]
4. Find [tex]\( x \)[/tex] using the value of [tex]\( y \)[/tex]:
Substitute [tex]\( y = 50 \)[/tex] back into the first equation [tex]\( x = 2y \)[/tex]:
[tex]\[
x = 2 \times 50
\][/tex]
Simplify the multiplication:
[tex]\[
x = 100
\][/tex]
5. Identify the solution:
[tex]\[
x = 100, \quad y = 50
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
(x, y) = (100, 50)
\][/tex]
Thus, from the given options, the correct solution is:
[tex]\[
(100, 50)
\][/tex]
