Question

System of Equations Solve with Elimination Method

1. x-3y=-5, x+3y=1
2. -x-y=-9, x-y=3
3. 2x+8y=22, 8x-8y=8
4. 4x-2y=-20, 7x+2y=-2
5. -2x-8y=-16, 2x-7y=-14
6. 4x-3y=1, -8x+6y=-2
7. -x+2y=21, 5x+6y=23

Answer 1

(4.4, 5.4), (3.2, 8.3), (-7, 15), (23 4/15, 2 7/15)

Explanation:

1.

Multiply the first equation by 3/2:

3/2×8x + 3/2×2y = 3/2×46

12x + 3y = 69

Subtract the second equation:

12x - 7x = 69 - 47

5x = 22

x = 4.4

Find y:

4*4.4 + y = 23

y = 23 - 17.6

y = 5.4

2.

Double the second equation and subtract the first one:

14x - 4x = 94 - 62

10x = 32

x = 3.2

Find y:

4*3.2 + 6y = 62

6y = 62 - 12.8

6y = 49.8

y = 8.3

3.

Subtract the second equation from the first one:

4x - 2x = 62 - 76

2x = -14

x = -7

Find y:

4(-7) + 6y = 62

6y = 62 + 28

6y = 90

y = 15

4.

Multiply the second equation by 4 and subtract the first one:

16y - y = 4(98) - 43

15y = 349

y = 349/15

y = 23 4/15

Find x:

8x + 23 4/15 = 43

8x = 19 11/15

x = 2 7/15

Answer 2

x - 3y = -5
x + 3y = 1
-------------add
2x = -4
x = -4/2
x = -2

x - 3y = -5
-2 - 3y = -5
-3y = -5 + 2
-3y = -3
y = -3/-3
y = 1

solution is (-2,1)
====================
-x - y = -9
x - y = 3
-------------add
-2y = - 6
y = -6/-2
y = 3

x - y = 3
x - 3 = 3
x = 3 + 3
x = 6

solution is (6,3)
==================
2x + 8y = 22
8x - 8y = 8
---------------add
10x = 30
x = 30/10
x = 3

2x + 8y = 22
2(3) + 8y = 22
6 + 8y = 22
8y = 22 - 6
8y = 16
y = 16/8
y = 2

solution is (3,2)
==================
4x - 2y = -20
7x + 2y = -2
--------------add
11x = -22
x = -22/11
x = -2

7x + 2y = -2
7(-2) + 2y = -2
-14 + 2y = -2
2y = -2 + 14
2y = 12
y = 12/2
y = 6

solution is (-2,6)
====================
-2x - 8y = -16
2x - 7y = -14
-----------------add
-15y = -30
y = -30/-15
y = 2

2x - 7y = -14
2x - 7(2) = -14
2x - 14 = -14
2x = -14 + 14
2x = 0
x = 0

solution is (0,2)
=================
4x - 3y = 1
-8x + 6y = -2...reduce by dividing by -2...giving u 4x - 3y = 1
same lines....infinite solutions
==================
-x + 2y = 21......multiply by 5
5x + 6y = 23
----------------
-5x + 10y = 105 (result of multiplying by 5)
5x + 6y = 23
----------------add
16y = 128
y = 128/16
y = 8

-x + 2y = 21
-x + 2(8) = 21
-x + 16 = 21
-x = 21 - 16
-x = 5
x = -5

solution is (-5,8)