Question

question 13 of 25
at what point do the graphs of the lines $4x + 3y = 7$ and $x + 2y = -2$ intersect?
\bigcirc\\ (0, -1)
\bigcirc\\ (6, -4)
\bigcirc\\ (1, 1)
\bigcirc\\ (4, -3)

Explanation:

Step1: Solve the second equation for x

From \( x + 2y = -2 \), we get \( x = -2 - 2y \).

Step2: Substitute x into the first equation

Substitute \( x = -2 - 2y \) into \( 4x + 3y = 7 \):
\( 4(-2 - 2y) + 3y = 7 \)
\( -8 - 8y + 3y = 7 \)
\( -8 - 5y = 7 \)

Step3: Solve for y

Add 8 to both sides: \( -5y = 15 \)
Divide by -5: \( y = -3 \)

Step4: Substitute y back to find x

Substitute \( y = -3 \) into \( x = -2 - 2y \):
\( x = -2 - 2(-3) = -2 + 6 = 4 \)

Answer:

(4, -3)