Math problems. Please help me!!!?

Question

I need help with thse problems.
Solve the system using elimination method.

1. 2x+6y=17
2x-10y=9

2. 4x-2y=-16
-3x+4y=12

3. 3x-4y= -10
6x+3y= -42

Answer 1

1)

eliminatkon by addition method

2x + 6y = 17- - - - - -Equation 1
2x - 10y = 9- - - - - - Equatioh 2
- - - - - - - - - -

Multiply equation 2 by - 1

2x - 10y = 9

- 1(2x) - (- 1)10y) = -1(9)

- 2x - (- 10y = - 9

1 2x + 10y = - 9. . .new equation 2

combine equation 1 with new equation 2

2x + 6y = 17
- 2x + 10y = - 9
- - - - - - - - -
16y = 8

Divide both sides of the equation by 16

16y / 16 = 8 / 16

y = 8/16

y = 1/2

Insert the y value into equation 1
- - - - - - - - - -

2x + 6y = 17

2x + 6(1/2) = 17

2x + 6/3 = 17

2x + 3 = 17

Transpose 3

2x + 3 - 3 = 17 - 3

Collect like terms

2x = 14

Divide both sides of the equation by 2

2x / 2 = 14 / 2

x = 14/2

x = 7

Insert the x value into equation 1
- - - - - - - - - -

Check for equation 1

2x + 6y = 17

2(7) + 6(1/2) = 17

14 + 6/2 = 17

14 + 3 = 17

17 = 17

- - - - - - - -

Check for equation 2

2x - 10y = 9

2(7) - 10(1/2) = 9

14 - 10/2 = 9

14 - 5 = 9

9 = 9

- - - - - - - -

both equations balance

The solutio set is { 7, 1/2 }

- - - - - - -s-

Answer 2

1.

a) 2x+6y=17
b) 2x-10y=9

Subtract equation b from equation a to eliminate x

16y = 8
y = 1/2

Use either a or b to solve for x

a) 2x + 6(1/2) = 17
2x + 3 = 17
2x = 14
x = 7

Check

b) 2x-10y=9
2(7) - 10(1/2) = 9
14 - 5 = 9
9 = 9

2.

a) 4x-2y=-16
b) -3x+4y=12

Multiply equation a by 2 and add that result to equation b to eliminate y


3.

a) 3x-4y= -10
b) 6x+3y= -42

Multiply equation a by -2 and add the result to equation b to eliminate x

Answer 3

Ok, on the first one, they are both 2x so multiply one of them by (-). Then add. So the x's take care of themselves. You have 16y =8 so y =1/2. Then just put the Y into the equation and figure out X. Problem 2, use the same method, just look for y first. Multiply the top one by 2 so that you have a comon y variable which is going to be 4. I don't want to give you the answers, but hopefully this will help.

Answer 4

First system, multiply the first equation by -1 then combine the equations to eliminate the x-term

-16y = -8 divide both sides by -16 and get

y = 1/2 substitue the value of y into either equation and solve for x and get x = 7

second system multiply the first equation by -2 and combine

-7x = 28 divide both sides by -7 and get x = -4; substitute and solve for y and get y = 0

third system multply first equation by -2 and combine to get
8y = -32 divide both side by 8 and get

y= -4 substitute and solve for x and get x = -5

Answer 5

3.
1) 3x-4y= -10
2)6x+3y= -42

2X 1) 6x-8y = -20
......2) 6x+3y= -42........subtract
=> -11y = 22
=> y = -2

plug into 1) or 2) to find x