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How do you solve the following system: $2 x - 6 y = - 12, 2 x + y = 8$ $2x-6y=-12 , 2x + y = 8$ ?

1 Answer

Feb 4, 2016

$(x, y) = (\frac{18}{7}, \frac{20}{7})$ $(x,y)=(18/7,20/7)$

Explanation:

Given:
[1] $XXX 2 x - 6 y = - 12$ $color(white)("XXX")2x-6y=-12$
[2] $XXX 2 x + y = 8$ $color(white)("XXX")2x+y=8$

Subtract equation [1] from equation [2] to get:
[3] $XXX 7 y = 20$ $color(white)("XXX")7y=20$

Divide both sides of equation [3] by $7$ $7$ :
[4] $XXX y = \frac{20}{7}$ $color(white)("XXX")y=20/7$

Substitute $\frac{20}{7}$ $20/7$ , the value given for $y$ $y$ in equation [4], for $y$ $y$ in equation [2]
[5] $XXX 2 x + \frac{20}{7} = 8$ $color(white)("XXX")2x+20/7=8$

Subtract $\frac{20}{7}$ $20/7$ from both sides of equation [5] and simplify the right side
[6] $XXX 2 x = 8 - \frac{20}{7} = \frac{56}{7} - \frac{20}{7} = \frac{36}{7}$ $color(white)("XXX")2x=8-20/7 = 56/7-20/7 = 36/7$

Divide both sides of equation [6] by $2$ $2$
$XXX x = \frac{18}{7}$ $color(white)("XXX")x=18/7$

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