Question

solve the following system of equations.
2x + 9y = 14
3x - 7y = -20
x =
y =

Explanation:

Step1: Eliminate x by scaling equations

Multiply first equation by 3: \( 6x + 27y = 42 \)
Multiply second equation by 2: \( 6x - 14y = -40 \)

Step2: Subtract equations to solve y

Subtract the two new equations:
\( (6x + 27y) - (6x - 14y) = 42 - (-40) \)
\( 41y = 82 \)
\( y = \frac{82}{41} = 2 \)

Step3: Substitute y=2 into first equation

Substitute \( y = 2 \) into \( 2x + 9y = 14 \):
\( 2x + 9(2) = 14 \)
\( 2x + 18 = 14 \)
\( 2x = -4 \)
\( x = -2 \)

Answer:

\( x = -2 \), \( y = 2 \)