Here we go all (Addition)?

Question

1/2 x - 1/3y = 5/6
- 2/5x + 1/2 y = - 9/10

Answer 1

Multiply the first equation by 6 and the second equation by 10 to get rid of the fractions:
6(1/2x-1/3y=5/6)
10(-2/5x+1/2y=-9/10)

3x-2y=5
-4x+5y=-9

Multiply the first equation by 5 and the second equation by 2:
15x-10y=25
-8x+10y=-18
=========
7x=7
x=1

15(1)-10y=25
15-10y=25
-10y=10
y=-1

The solution set is (1,-1)

Check:
1/2(1)-1/3(-1)=5/6
1/2+1/3=5/6
3/6+2/6=5/6
5/6=5/6

-2/5(1)+1/2(-1)=-9/10
-2/5-1/2=-9/10
-4/10-5/10=-9/10
-9/10=-9/10

I hope this helps!

Answer 2

First, let's get rid of the denominators, just for sake of simplifying the calculations.

1/2 x - 1/3y = 5/6
- 2/5x + 1/2 y = - 9/10

Multiplying both sides of the first equation by 6, and both sides of the second equation by 10:

3x - 2y = 5
-4x + 5y = -9

At once, I see that x = 1 and y = -1, but let's do this one "by the book"; I suppose that the teacher wants this one solved by the addition method.

I will get rid of the x. Multiply the first equation by 4 and the second equation by 3:

3x - 2y = 5
-4x + 5y = -9

12x - 8y = 20
-12x + 15y = -27

Adding the equations,
-8y + 15y = 20 - 27
7y = -7
y = -1

Substituting y back into one of the equations,
3x - 2y = 5
3x + 2 = 5
3x = 3
x = 1

Solution: x = 1, y = -1.

Answer 3

1/2 x - 1/3y = 5/6
- 2/5x + 1/2 y = - 9/10
Multiply 1st equation by 1/2 and 2nd equation by 1/3 getting:
1/4 x - 1/6 y = 5/12
-2/15 x +1/6 y = - 3/10
Add the above equations, getting:
7/60 x = 7/60
x = 1
1/2(1) -1/3 y =5/6
y = -3(5/6 -1/2) = -1

Answer 4

To solve by adding the equations, you need to multiply both equations by something so that one of the variables will cancel out. I choose cancelling the y's, so I multiply the top equation by 3 and the bottom by 2

3/2 x - 3/3 y = 5/2
-4/5 x + 2/2 y = -9/5

15/10 x - y = 25/10
-8/10 x + y = -18/10
-----------------------------
7/10 x = 7/10
x = 1 (multiply by 10/7)

Then substitute into one of the equations:

15/10 x - y = 25/10
15/10 - y = 25/10
- y = 10/10
y = -1

Solution is {1,-1}

Answer 5

ok, so use the first equation to solve for either x or y. let's go with x for now.

1/2 x=5/6+1/3 y
x= 5/4+2/3y

then, plug that equation in for x in the second equation.

-2/5(5/4 +2/3y) +1/2y =-9/10
so
y=-12/7
now plug this value of y back in to the first equation to solve for x.

i think that should all be correct, but some of the actual math might be off. the steps are definitley correct, however. as long as you solve for it and don't mess up any of the addition, subtraction, multiplication, or division, you'll be fine.

Answer 6

Multiply first eqn by 6 and second by 10

3x - 2y = 5
-4x+5y = -9
Multiply first eqn by 4 and second by 3
12x - 8y =20
-12x +15y = -27

Add
7y = -7
y = -1
Substitute in above eqn
x = 1