Question

solve the system by substitution.
$3x + 4y = 50$
$-2x = y$

Explanation:

Step1: Substitute \( y = -2x \) into the first equation

We have the first equation \( 3x + 4y = 50 \) and the second equation gives \( y = -2x \). Substitute \( y \) in the first equation:
\( 3x + 4(-2x) = 50 \)

Step2: Simplify and solve for \( x \)

Simplify the left - hand side:
\( 3x-8x = 50 \)
Combine like terms:
\( - 5x=50 \)
Divide both sides by - 5:
\( x=\frac{50}{-5}=- 10 \)

Step3: Substitute \( x = - 10 \) into \( y=-2x \) to find \( y \)

Substitute \( x=-10 \) into \( y = - 2x \):
\( y=-2\times(-10)=20 \)

Answer:

The solution of the system is \( x = - 10 \), \( y = 20 \)