Algebra 2 Solving Linear Systems?

Question

Please use the linear combination method or substitution method (would appreciate if linear combination i am having more troubles with that) to solve these problems i couldn't figure it out.. please and show a few steps of work i would greatly appreciate it. (Each comma seperates the 2 equations)

1) -3x+y=11, 5x-2y= -16

2) 3x-7y = 20 , -11x+10y = 5

3) 1/3x + y= 9, -2x+2y=-6

4) -x+5y=17, 2x-10y = -34

5) -2x+3y=20, 4x+4y = -15

Duffy did u use combination or subsitution method?

Answer 1

1) -3x + y = 11.............eqtn (1)

5x - 2y = -16.................eqtn(2)

From (1), y = 11 + 3x. Now substitute this into eqtn (2), to give one eqtn with one unknown:

5x - 2y = -16, so

5x - 2(11 + 3x) = -16, so

5x - 22 - 6x = -16, so

-x - 22 = -16, so

-x = -16 + 22, so

-x = 6, so

x = -6.

y = 11 + 3x, so

y = 11 + 3(-6), so

y = 11 - 18, so

y = -7

Hope this helps, Twiggy.

Answer 2

Elimination by addition method

- 3x + y = 11- - - - - - Equation 1
5x - 2y = - 16- - - - - -Equation 2
- - - - - - - - - - -
Multiply equaton 1 by 2

- 3x + y = 11

- 2(3x) + 2(y) = 2(11)

- 6x + 2y = 22. . .New equation 1

Combine new equation 1 with equation 2
- - - - - - - - - - - - -

Elimination of y

- 6x + 2y = 22
5x - 2y = - 16
- - - - - - - - - --

- x = 6

Multiply both sides of the equation by - 1

- 1(- x) = - 1(6)

- ( - x ) = - 6

x = - 6

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

- 3x + y = 11

- 3( - 6) + y = 11

- ( - 18) + y = 11

18 + y = 11

Transpose 18

18 + y - 18 = 11 - 18

y = - 7

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

Check for equation 1

- 3x + y = 11

- 3( - 6) + ( - 7) = 11

- ( - 18) - 7 = 11

18 - 7 = 11

11 = 11

- - - - - - - - - -

Check for equation 2

5x - 2y = - 16

5(- 6) - 2( - 7) = - 16

- 30 - ( - 14) = - 16

- 30 + 14 = - 16

- 16 = - 16

- - - - - - - - -

Both equations balance

The solution set is { - 6, - 7 }

- - - - - - -s-

Answer 3

2. 3x - 7y = 20 and -11x + 10y = 5
Multiply equation 1 by 11
33x - 77y = 220
Multiply equation 2 by 3
-33x + 30y = 15
Add equation 1 and equation 2
0x - 47y = 235
Divide by -47
y = -5
Use either equation to solve for x
3x - 7(-5) = 20
3x + 35 = 20
3x = -15
x = -5

You can check your solution in the other equation:
-11(-5) + 10(-5) = 5
55 - 50 = 5
5 = 5

The results are correct.

3. 1/3 (x) + y = 9, -2x + 2y = -6
To "get rid" of your fraction in equation 1 and to have the coefficient of the "x" term equal the opposite of the coefficient of the "x" term in equation 2, multiply equation 1 by 6:
2x + 6y = 54
add this to equation 2
0x + 8y = 48
divide by 8
y = 6

-2x + 2(6) = -6
-2x + 12 = -6
-2x = -18
x = 9

Checking your solution
1/3(9) + 6 = 9
3 + 6 = 0
9 = 9

4. -x + 5y = 17, 2x - 10y = -34
Multiply equation 1 by 2 and add to equation 2
-2x + 10y = 34
2x -10y = -34
0 = 0
which means your lines are co-linear (they are the same). Both have the same slope and y-intercept.

5. -2x + 3y = 20, 4x + 4y = -15
Multiply equation 1 by 2
-4x + 6y = 40
add to equation 2
10y = 25
y = 25/10

Substitute in equation 1
-2x + 3(25/10) = 20
-2x + 75/10 = 20
Multiply by 10
-20x + 75 = 200
-20x = 125
x = -125/20

Checking in equation 2
4(-125/20) + 4(25/10) = -15
-125/5 + 100/10 = -15
-25 + 10 = -15
-15 = -15

Answer 4

5x + 2 = 3x set them equal to each other 2x = -2 x = -1 y = 3(-1) or y = (5(-1)) + 2 y = -3 (-1,-3)