To solve the system of equations using substitution, follow these steps:
Given equations:
1. \(3x + 2y = 7\)
2. \(y = -3x + 11\)
Substitute the expression for \(y\) from the second equation into the first equation:
\[
3x + 2(-3x + 11) = 7
\]
Distribute the 2 in the second term:
\[
3x - 6x + 22 = 7
\]
Combine like terms:
\[
-3x + 22 = 7
\]
Isolate \(x\) by subtracting 22 from both sides:
\[
-3x = 7 - 22
\]
Simplify:
\[
-3x = -15
\]
Divide both sides by -3:
\[
x = 5
\]
Now, substitute \(x = 5\) into the second equation to find \(y\):
\[
y = -3(5) + 11
\]
\[
y = -15 + 11
\]
\[
y = -4
\]
So, the solution to the system of equations is:
\[
(x, y) = (5, -4)
\]
Therefore, the correct answer is \( (5, -4) \).
1.
Solve the system of equations using substitution.
3x + 2y = 7
y = –3x + 11
(5, –4)
(6, –3)
(6, –7)
1 answer