4x + 3y = 7

Question

2x + 7y = -13

What is the solution to the system of equations above?
Responses
A x = 4, y = -3x = 4, y = -3
B x = -4, y = 2x = -4, y = 2
C x = -3, y = -4x = -3, y = -4
D x = 2, y = -3

Answer 1

To solve the system of equations:

1. \( 4x + 3y = 7 \) (Equation 1)
2. \( 2x + 7y = -13 \) (Equation 2)

We can use the substitution or elimination method. Here, we will use the elimination method.

First, we can multiply Equation 1 by 2 to align the coefficients of \(x\):

\[ 2(4x + 3y) = 2(7) \implies 8x + 6y = 14 \quad \text{(Equation 3)} \]

Now, we have the modified equations:

1. \( 8x + 6y = 14 \) (Equation 3)
2. \( 2x + 7y = -13 \) (Equation 2)

Next, we can multiply Equation 2 by 4 to align the coefficients of \(x\):

\[ 4(2x + 7y) = 4(-13) \implies 8x + 28y = -52 \quad \text{(Equation 4)} \]

Now, we subtract Equation 3 from Equation 4:

\[ (8x + 28y) - (8x + 6y) = -52 - 14 \]

This simplifies to:

\[ 22y = -66 \]

Solving for \(y\):

\[ y = -3 \]

Now, we substitute \(y = -3\) back into Equation 1 to find \(x\):

\[ 4x + 3(-3) = 7 \] \[ 4x - 9 = 7 \] \[ 4x = 16 \] \[ x = 4 \]

Thus, the solution to the system of equations is \(x = 4\) and \(y = -3\).

Therefore, the answer is: A) \(x = 4, y = -3\)