To solve the given system of equations using the substitution method, we follow these steps:
[tex]\[
\begin{array}{l}
\left\{\begin{array}{l}
3x + y = 3 \\
2x - 5y = 6
\end{array}\right.
\end{array}
\][/tex]
1. Isolate [tex]\( y \)[/tex] in the first equation:
[tex]\[
3x + y = 3
\][/tex]
Subtract [tex]\( 3x \)[/tex] from both sides to express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[
y = 3 - 3x
\][/tex]
2. Substitute [tex]\( y \)[/tex] in the second equation:
Replace [tex]\( y \)[/tex] with the expression [tex]\( 3 - 3x \)[/tex] in the second equation:
[tex]\[
2x - 5(3 - 3x) = 6
\][/tex]
3. Solve the substituted equation for [tex]\( x \)[/tex]:
First, distribute the [tex]\(-5\)[/tex] through the parentheses:
[tex]\[
2x - 5 \cdot 3 + 5 \cdot 3x = 6
\][/tex]
Simplify inside the parentheses:
[tex]\[
2x - 15 + 15x = 6
\][/tex]
Combine like terms:
[tex]\[
17x - 15 = 6
\][/tex]
Add 15 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
17x = 21
\][/tex]
Divide both sides by 17 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{21}{17}
\][/tex]
So, the value of [tex]\( x \)[/tex] in the system of equations is [tex]\( \frac{21}{17} \)[/tex].
