How do solve the following linear system?: -x+3y=-5 , 2x+7=-5y −x+3y=−5,2x+7=−5y?

1 Answer
Tony B
Mar 19, 2016

I have taken you to a point where you can solve for xx
color(red)(y=-17/11)y=−1711

Explanation:

Given:
-x+3y= -5−x+3y=−5 ...............................(1)
2x+7=-5y2x+7=−5y.................................(2)

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To solve a single equation you can only do so it contains only one unknown. So to solve any of these two we need to 'get rid of a variable'

Look at equation (1). We have a single xx. So this is the simpler of the two to use as a source of values for substitution.

color(blue)("Solving for y")Solving for y

Consider equation (1)

Multiply by (-1) to make the xx positive

x-3y=+5x−3y=+5

Add 3y3y to both sides

color(green)(x=3y+5)" "............................(1_a)

Substitute for x in equation (2) using equation (1_a)

color(brown)(2x+7=-5y" "color(blue)(->" "2(color(green)(3y+5))+7=-5y)

6y+10+7=-5y

6y+5y=-17

color(red)(y=-17/11) ...................................(3)
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Substitute equation (3) into equation (1) or (2). You chose!

I will let you finish this off.

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