Solve simple equations?

Question

solve the given pairs of equations simultaneously.
a) 4x+4y= -12 ; -2x+3y= 14
b) 3x+2y=5 ; 2x-3y=3

Answer 1

a)
4x + 4y = -12
-2x + 3y = 14

Double the second equation and add:
4x + 4y = -12
-4x + 6y = 28
10y = 16
y = 16/10
y = 8/5

Then solve for x:
x + (8/5) = -3
x = -3 - 8/5
x = -4 3/5

b)
3x + 2y = 5
2x - 3y = 3

Multiply the top by 2 and the bottom by 3, then subtract:
6x + 4y = 10
6x - 9y = 9
13y = 1
y = 1/13

Then solve for x:
3x + 2(1/13) = 5
3x + 2/13 = 5
3x = 63/13
x = 21/13
x = 1 8/13

Answer 2

I find the easiest way of solving this problem is by cheating and copying this chaps work that looks about right not that I would know in any case, but he seems to have a good handle on this subject:

a)
4x + 4y = -12
-2x + 3y = 14

Double the second equation and add:
4x + 4y = -12
-4x + 6y = 28
10y = 16
y = 16/10
y = 8/5

Then solve for x:
x + (8/5) = -3
x = -3 - 8/5
x = -4 3/5

b)
3x + 2y = 5
2x - 3y = 3

Multiply the top by 2 and the bottom by 3, then subtract:
6x + 4y = 10
6x - 9y = 9
13y = 1
y = 1/13

Then solve for x:
3x + 2(1/13) = 5
3x + 2/13 = 5
3x = 63/13
x = 21/13
x = 1 8/13

Answer 3

a) Look for ways of getting rid of one of the two unknowns. Notice the -2x in the second equation, if it were doubled it would match the 4x in the first equation, so:

Multiply (both sides of) the second equation by 2:
-4x + 6y = 14

Now add this equation to the first one (that means add their left sides together, put "=" , and add their right sides together) and you then have an equation with y as the only unknown. Solve this, then sub the value of y into one of the original equations, I suggest the first one, which you can then solve to find x.

b) Not quite so obvious, but if you multiply the first equation by 3 and the second by 2, you'll have +6y in the first and -6y in the second, so when you add them together you'll have an equation with x as the only unknown. Solve, sub the value you find for x in the first equation and solve it to find y.

Now I see a couple of people have already done it for you, but you'd still better do it for yourself after seeing what to do.