Question

solve the system by substitution.
2x + 5y = 7
x = -4y + 5
the solution is (\square, \square ).

Explanation:

Step1: Substitute \( x = -4y + 5 \) into \( 2x + 5y = 7 \)

Substitute \( x \) in the first equation: \( 2(-4y + 5) + 5y = 7 \)

Step2: Simplify and solve for \( y \)

Expand: \( -8y + 10 + 5y = 7 \)
Combine like terms: \( -3y + 10 = 7 \)
Subtract 10: \( -3y = 7 - 10 = -3 \)
Divide by -3: \( y = \frac{-3}{-3} = 1 \)

Step3: Substitute \( y = 1 \) into \( x = -4y + 5 \)

Find \( x \): \( x = -4(1) + 5 = -4 + 5 = 1 \)

Answer:

(1, 1)