Question

Solve the system by substitution.

2x+y=−11


3x−4y=11


(1 point)
Responses

(5,3)
open paren 5 comma 3 close paren

(−5,−3)
open paren negative 5 comma negative 3 close paren

(3,5)
open paren 3 comma 5 close paren

(−3,−5)
open paren negative 3 comma negative 5 close paren

Answer 1

To solve the system of equations by substitution, we start with the given equations:

1. \( 2x + y = -11 \) (Equation 1)
2. \( 3x - 4y = 11 \) (Equation 2)

First, we can solve Equation 1 for \( y \):

\[
y = -11 - 2x
\]

Next, we substitute this expression for \( y \) into Equation 2:

\[
3x - 4(-11 - 2x) = 11
\]

Now, we simplify the equation:

\[
3x + 44 + 8x = 11
\]

Combining like terms, we get:

\[
11x + 44 = 11
\]

Next, we isolate \( x \) by moving 44 to the other side:

\[
11x = 11 - 44
\]
\[
11x = -33
\]
\[
x = -3
\]

Now that we have \( x = -3 \), we substitute this value back into the expression we found for \( y \):

\[
y = -11 - 2(-3)
\]
\[
y = -11 + 6
\]
\[
y = -5
\]

So, the solution to the system of equations is:

\[
(x, y) = (-3, -5)
\]

Thus, the answer is:

\[
\text{(−3,−5)}
\]