Question

solve the system by substitution.
3x = y
-5x - 10y = -35

Explanation:

Step1: Substitute \( y = 3x \) into the second equation

We know from the first equation \( 3x = y \), so we substitute \( y \) in the second equation \( -5x - 10y = -35 \) with \( 3x \). This gives us \( -5x - 10(3x) = -35 \).

Step2: Simplify and solve for \( x \)

First, simplify the left - hand side of the equation: \( -5x-30x=-35 \). Combine like terms: \( -35x = - 35 \). Then, divide both sides by \( -35 \): \( x=\frac{-35}{-35}=1 \).

Step3: Substitute \( x = 1 \) back into the first equation to find \( y \)

Since \( y = 3x \) and \( x = 1 \), then \( y=3\times1 = 3 \).

Answer:

The solution to the system of equations is \( x = 1 \) and \( y = 3 \), or in ordered - pair form \( (1,3) \).