To solve the system of equations using the substitution method, follow these steps:
Given equations:
1. [tex]\( 2x + 3y = 11 \)[/tex]
2. [tex]\( y = x - 3 \)[/tex]
Step 1: Substitute the expression for [tex]\( y \)[/tex] from the second equation into the first equation.
[tex]\[
2x + 3(x - 3) = 11
\][/tex]
Step 2: Distribute and combine like terms.
[tex]\[
2x + 3x - 9 = 11
\][/tex]
Step 3: Combine the [tex]\( x \)[/tex] terms.
[tex]\[
5x - 9 = 11
\][/tex]
Step 4: Add 9 to both sides to isolate the [tex]\( x \)[/tex] term.
[tex]\[
5x - 9 + 9 = 11 + 9
\][/tex]
[tex]\[
5x = 20
\][/tex]
Step 5: Divide both sides by 5 to solve for [tex]\( x \)[/tex].
[tex]\[
x = \frac{20}{5}
\][/tex]
[tex]\[
x = 4
\][/tex]
Step 6: Substitute the value of [tex]\( x \)[/tex] back into the second equation to find [tex]\( y \)[/tex].
[tex]\[
y = x - 3
\][/tex]
[tex]\[
y = 4 - 3
\][/tex]
[tex]\[
y = 1
\][/tex]
Therefore, the solution to the system of equations is the ordered pair [tex]\((4, 1)\)[/tex].
Thus, the correct choice is:
C. [tex]\((4, 1)\)[/tex]
