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11x+15y+23=0, 7x-2y-20=0

I tried,

11x+15y+23=0------1

7x-2y-20=0-----------2

11x+15y=-23

=>y=-23x-11x/15 (substituting the value of y in eq 2)

11x+15(-23x-11x/15)=20

The correct way to try that is to say

1) 11x + 15y + 23 = 0

2) 7x - 2y - 20 = 0.

Correctly solving the 1st equation for x gives ...

Subtract off 11x + 23 from both sides, giving 15y = -23 - 11x.

Divide by 15, giving y = -23/15 - 11x/15.

Put that into (2) for y and solve. That gives 7x - 2(-23/15) -2(-11x/15) - 20 = 0.

The negatives in the 2nd terms cancel, giving 2(23/15),and

the negatives in the 3rd equation cancel, giving 2(11x/15).

Note that 2(23/15) = 46/15 and 2(11x/15) = 22x/15, so the equation

7x - 2(-23/15) -2(-11x/15) - 20 = 0 turns into 7x + 46/15 + 22x/15 - 20 = 0.

Since 7x is really 105x/15 and -20 is -300/15, we can put those in and get

105x/15 + 46/15 + 22x/15 - 300/15 = 0.

Multiplying both sides by 15 drops all the fractions and we are left with

105x + 46 + 22x - 300 = 0.

Combining like terms gives (105+22)x + 46-300 = 0.

That reduces to 127x – 254 = 0.

Adding 254 to both sides gives 127x = 254.

Dividing both sides by 127 gives x = 2.

Using equation (1), we then solve for y. Putting in x=2 gives 22 + 15y + 23 = 0.

Since 22+23=45, we have 45+15y=0. Subtracting 45 from both sides gives 15y=-45.

Dividing both sides by 15 gives y=-3.

Taking x=2 and y =-3, the 2nd equation can be used to check.

The left side gives 7(2) -2(-3) – 20 = 14 + 6 – 20 = 20 – 20 = 0,

and that’s what is on the right side, so this has been done correctly.

Algebra

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