How do you solve the system 5x - y = - 14 + 2x + y and 7x + 9y + 4 = 3x + 8y?

1 Answer
Suren Abreu
Feb 6, 2017

x=-2 and y=4

Explanation:

First simplify both equations:
5x-y=-14+2x+y

Subtract 2x and y from both sides.

3x-2y=-14

color(red)(7x+9y+4=3x+8y)

Subtract 3x and 8y from both sides.

color(red)(4x+y+4=0)

Subtract 4 from each side.

color(red)(4x+y=-4)

So now we have two simplified equations:
3x-2y=-14
color(red)(4x+y=-4)

Using the second equation, determine a value for y.

color(red)(4x+y=-4)

Subtract 4x from both sides.

color(red)(y=-4-4x)

In the first equation, substitute y with color(red)((-4-4x)).

3x-2y=-14

3x-2color(red)((-4-4x))=-14

Open the brackets and simplify. The product of two negatives results in a positive.

3x+color(red)(8+8x)=-14

11x+8=-14

Subtract 8 from each side.

11x=-22

Divide both sides by 11.

x=-2

In the second equation, substitute x with color(blue)(-2).

color(red)(4x+y=-4)

color(red)(4color(blue)((-2))+y=-4)

Open the brackets and simplify. The product of a positive and a negative results in a negative.

color(red)(-8+y=-4)

Add 8 to both sides.

color(red)(y=4)

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