Question

solve the system by substitution.
2x + 3y = 5
y = 5x - 4
the solution is (\square, \square).

Explanation:

Step1: Substitute \( y = 5x - 4 \) into \( 2x + 3y = 5 \)

We know \( y = 5x - 4 \), so replace \( y \) in the first equation: \( 2x + 3(5x - 4) = 5 \)

Step2: Simplify and solve for \( x \)

Expand the equation: \( 2x + 15x - 12 = 5 \)
Combine like terms: \( 17x - 12 = 5 \)
Add 12 to both sides: \( 17x = 5 + 12 = 17 \)
Divide by 17: \( x = \frac{17}{17} = 1 \)

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

\( y = 5(1) - 4 = 5 - 4 = 1 \)

Answer:

\( (1, 1) \)