To find the value of [tex]\( x \)[/tex] in the given system of equations, let's follow a step-by-step substitution method.
We are given:
[tex]\[ y = 3x + 5 \][/tex]
[tex]\[ 2x + y = 10 \][/tex]
First, we'll substitute [tex]\( y \)[/tex] from the first equation into the second equation.
1. Start with the second equation:
[tex]\[ 2x + y = 10 \][/tex]
2. Substitute [tex]\( y \)[/tex] from the first equation [tex]\( y = 3x + 5 \)[/tex]:
[tex]\[ 2x + (3x + 5) = 10 \][/tex]
3. Combine like terms:
[tex]\[ 2x + 3x + 5 = 10 \][/tex]
[tex]\[ 5x + 5 = 10 \][/tex]
4. Subtract 5 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 5x + 5 - 5 = 10 - 5 \][/tex]
[tex]\[ 5x = 5 \][/tex]
5. Divide both sides by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 1 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] after substitution is [tex]\( 1 \)[/tex].
The answer is:
[tex]\[ \boxed{1} \][/tex]
