Question

what is the solution to the system of equations?
2x + 3y = 26
3x + 5y = 40
x = 10, y = 2
x = 10, y = -2
x = -10, y = -2
x = -10, y = 2

Explanation:

Step 1: Check \( x = 10, y = 2 \) in \( 2x + 3y \)

Substitute \( x = 10 \) and \( y = 2 \) into \( 2x + 3y \):
\( 2(10) + 3(2) = 20 + 6 = 26 \), which matches the first equation.

Step 2: Check \( x = 10, y = 2 \) in \( 3x + 5y \)

Substitute \( x = 10 \) and \( y = 2 \) into \( 3x + 5y \):
\( 3(10) + 5(2) = 30 + 10 = 40 \), which matches the second equation.

Other options fail:

• \( x = 10, y = -2 \): \( 2(10) + 3(-2) = 20 - 6 = 14

eq 26 \).

• \( x = -10, y = -2 \): \( 2(-10) + 3(-2) = -20 - 6 = -26

eq 26 \).

• \( x = -10, y = 2 \): \( 2(-10) + 3(2) = -20 + 6 = -14

eq 26 \).

Answer:

A. \( x = 10, y = 2 \)