i) Solve the simultaneous equations 4x + 3y + 4 = 0, 3x - 12y + 22 = 0.   Could you please teach me step by step, so that I can understand easily and without any problem? Thank you. :)

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4x + 3y + 4 = 0, 3x - 12y + 22 = 0.

I think the easiest way to do this is by addition.  So we need to make it so two of the variables (one each from each equation) will come to 0 when we add them.

I...

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4x + 3y + 4 = 0, 3x - 12y + 22 = 0.

I think the easiest way to do this is by addition.  So we need to make it so two of the variables (one each from each equation) will come to 0 when we add them.

I think the best way to do this is to multiply the first equation by 4 because then we will have 12y to cancel the -12y in the other equation.

So we multiply by 4 and we have

16x + 12y + 16

Now we add that equation to the other.  We add the like terms together.

16x + 3x is 19x

12y + (-) 12 y  is 0

16 + 22 is 38.

So we have 19x + 38 + 0

Move the 38 to the other side, we have

19x = -38

x = -2

Substitute that back into the first equation to solve for y.

4(-2) + 3y +4 = 0

-8 +3y +4 + 0

3y = 8 - 4

3y = 4

y = 4/3

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