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solve -2x+6y=6

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1 Answer

Hi Kristen;
-2x+6y=6
-7x+8y=-5
Let's select one equation and isolate one variable.
I randomly select the first equation and randomly select the variable x.
-2x+6y=6
Let's subtract 6y from both sides...
-6y+-2x+6y=-6y+6
-2x=-6y+6
Let's divide both sides by -2...
(-2x)/-2=(-6y+6)/-2
x=3y-3
Let's take the second equation and substitute x with 3y-3...
-7x+8y=-5
[(-7)(3y-3)]+8y=-5
(-21y+21)+8y=-5
-21y+21+8y=-5
-13y+21=-5
Let's subtract 21 from both sides...
-21-13y+21=-5-21
-13y=-26
Let's divide both sides by -13...
(-13y)/-13=-26/-13
A negative number divided by a negative number has a positive result...
y=2
Let's plug this into either equation to establish the value of x...
I randomly select the first equation...
-2x+6y=6
-2x+[(6)(2)]=6
-2x+12=6
Let's subtract 12 from both sides...
-12-2x+12=6-12
-2x=-6
Let's divide both sides by -2...
(-2x)/-2=-6/-2
x=3
Let's verify our results by plugging both values into the second equation...
-7x+8y=-5
[(-7)(3)]+[(8)(2)]=-5
-21+16=-5
-5=-5