Question

solve the system by substitution.\
\\(-2y = x\\)\
\\(7x + 9y = -45\\)

Explanation:

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

We know from the first equation that \( x = -2y \). Substitute this into \( 7x + 9y = -45 \), we get \( 7(-2y) + 9y = -45 \).

Step2: Simplify and solve for \( y \)

Simplify the left - hand side: \( 7(-2y)+9y=-14y + 9y=-5y \). So the equation becomes \( -5y=-45 \). Divide both sides by - 5: \( y=\frac{-45}{-5} = 9 \).

Step3: Substitute \( y = 9 \) back to find \( x \)

Substitute \( y = 9 \) into \( x=-2y \), we get \( x=-2\times9=-18 \).

Answer:

The solution of the system is \( x = - 18,y = 9 \)