To solve the given system of equations:
[tex]\[
10x - 9y = 24
\][/tex]
[tex]\[
y = x - 2
\][/tex]
we will use the second equation to substitute [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] into the first equation. Let's proceed step by step:
1. Start with the second equation:
[tex]\[
y = x - 2
\][/tex]
2. Substitute [tex]\( y \)[/tex] in the first equation:
[tex]\[
10x - 9(x - 2) = 24
\][/tex]
3. Distribute the -9 through the parentheses:
[tex]\[
10x - 9x + 18 = 24
\][/tex]
4. Simplify the equation:
[tex]\[
x + 18 = 24
\][/tex]
5. Solve for [tex]\( x \)[/tex] by subtracting 18 from both sides:
[tex]\[
x = 24 - 18
\][/tex]
[tex]\[
x = 6
\][/tex]
Now that we have [tex]\( x \)[/tex], we can substitute it back into the second equation to find [tex]\( y \)[/tex]:
6. Substitute [tex]\( x = 6 \)[/tex] into [tex]\( y = x - 2 \)[/tex]:
[tex]\[
y = 6 - 2
\][/tex]
[tex]\[
y = 4
\][/tex]
Therefore, the solutions to the system of equations are:
[tex]\[
x = 6
\][/tex]
[tex]\[
y = 4
\][/tex]
