Question

solve the system by substitution.\\(10x + 7y = -41\\)\\(-4x + 7 = y\\)

Explanation:

Step1: Substitute \( y = -4x + 7 \) into the first equation.

We have the first equation \( 10x + 7y = -41 \). Replace \( y \) with \( -4x + 7 \), so we get \( 10x + 7(-4x + 7) = -41 \).

Step2: Simplify and solve for \( x \).

First, expand the left - hand side: \( 10x-28x + 49=-41 \).
Combine like terms: \( -18x+49 = -41 \).
Subtract 49 from both sides: \( -18x=-41 - 49=-90 \).
Divide both sides by - 18: \( x=\frac{-90}{-18}=5 \).

Step3: Substitute \( x = 5 \) into the equation for \( y \).

We know that \( y=-4x + 7 \). Substitute \( x = 5 \) into this equation: \( y=-4\times5 + 7=-20 + 7=-13 \).

Answer:

The solution to the system is \( x = 5 \), \( y=-13 \)