Question

Solve the following system using the substitution method. Enter your answer as an ordered pair of form( x, y) 2x + 4y = -10.2 9x - 5y = 30

Answer 1

Given:

$\begin{gathered} 2x+4y=-10.2\ldots\ldots\ldots(1) \\ 9x-5y=30\ldots\ldots\ldots(2) \end{gathered}$

To solve for x and y:

Consider the equation (1),

$\begin{gathered} 2x+4y=-10.2 \\ 2x=-10.2-4y \\ x=-5.1-2y\ldots\ldots\ldots(3) \end{gathered}$

Substitute equation (3) in equation (2), we get

$\begin{gathered} 9(-5.1-2y)-5y=30 \\ -45.9-18y-5y=30 \\ -45.9-23y=30 \\ -23y=75.9 \\ y=-3.3 \end{gathered}$

Substitute y=-3.3 in equation (3) we get,

$\begin{gathered} x=-5.1-2(-3.3) \\ x=-5.1+6.6 \\ x=1.5 \end{gathered}$

Hence, the solution is,

$(1.5,-3.3)$