Answer:

1. ( 4, 7 )

2. ( 4, 9 )

3. ( -6, -2 )

4. ( -4, -8 )

5. ( -5, 9 )

6. ( 13, 6 )

7. ( 1, -6 )

8. ( 7, -9 )

9. ( 4, 3 )

10. ( -1, 5 )

Step-by-step explanation:

1. y = 6× - 17 -> 1st equation

3x - 6y = -30 -> 2nd equation

Substitute the 1st equation to the 2nd equation

3x - 6y = -30

3x - 6( 6x - 17 ) = -30

3x - [ 6 ( 6x ) + 6 ( -17 ) ] = -30

3x - 36x + 102 = -30

-33x = -30 - 102

-33x = -132

x = 4

y = 6x - 17

y = 6 ( 4 ) - 17 = 24 - 17 = 7

( 4, 7 )

2. y = 4x - 7 -> 1st equation

× + 8y = 76 -> 2nd equation

Substitute the 1st equation to the 2nd equation

x + 8y = 76

x + 8( 4x - 7 ) = 76

x + [ 8 ( 4x ) + 8 ( -7 ) ] = 76

x + 32x - 56 = 76

33x = 76 + 56

33x = 132

x = 4

y = 4x - 7

y = 4 ( 4 ) - 7 = 16 - 7 = 9

( 4, 9 )

3. × = y - 4 -> 1st equation

6x + 5y = -46 -> 2nd equation

Substitute the 1st equation to the 2nd equation

6x + 5y = -46

6( y - 4 ) + 5y = -46

6y - 24 + 5y = -46

11y = -46 + 24

11y = -22

y = -2

x = y - 4

x = -2 - 4 = -6

( -6, -2 )

4. y = 2x -> 1st equation

× - y = 4 -> 2nd equation

Substitute the 1st equation to the 2nd equation

x - y = 4

x - ( 2x ) = 4

-x = 4

x = -4

y = 2x

y = 2 ( -4 ) = -8

( -4, -8 )

5. 7x + y = -26

y = -26 - 7x -> 1st equation

12x + 11y = 39 2nd equation

Substitute the 1st equation to the 2nd equation

12x + 11y = 39

12x + 11( -26 - 7x ) = 39

12x - 286 - 77x = 39

-65x = 39 + 286

-65x = 325

x = -5

y = -26 - 7x

y = -26 - 7( -5 )

y = -26 + 35

y = 9

( -5, 9 )

6. × + y = 19

x = 19 - y -> 1st equation

x - y = 7 -> 2nd equation

Substitute the 1st equation to the 2nd equation

x - y = 7

( 19 - y ) - y = 7

19 - 2y = 7

-2y = 7 - 19

-2y = -12

y = 6

x = 19 - y

x = 19 - 6 = 13

( 13, 6 )

7.

-5x + 2y = -17

5x + 3y = -13

Solving by adding the two term to cancel out x

-5x + 5x + 2y + 3y = -17 + ( -13 )

5y = -17 - 13

5y = -30

y = -6

-5x + 2y = -17

-5x + 2 ( -6 ) = -17

-5x - 12 = -17

-5x = -17 + 12

-5x = -5

x = 1

( 1, -6 )

8. 8x + 6y = 2 -> 1st equation

2x - y = 23

-y = 23 - 2x

y = -23 + 2x -> 2nd equation

Substitute the 2nd equation to the 1st equation

8x + 6y = 2

8x + 6( -23 + 2x ) = 2

8x - 138 + 12x = 2

20x = 2 + 138

20x = 140

x = 140/20

x = 7

y = -23 + 2x

y = -23 + 2 ( 7 ) = -23 + 14 = -9

( 7, -9 )

9. x + 5y = 19

x + 2y = 10

Solving by subtracting the two term to cancel out x

x + 5y - ( x + 2y ) = 19 - ( 10 )

x + 5y - x - 2y = 19 - 10

5y - 2y = 9

3y = 9

y = 9/3

y = 3

x + 2y = 10

x + 2 ( 3 ) = 10

x + 6 = 10

x = 10 - 6 = 4

( 4, 3 )

10. 7x + 3y = 8 -> 1st equation

5x - 4y = -25

5x = -25 + 4y

x = ( -25 + 4y )/5 -> 2nd equation

Substitute the 2nd equation to the 1st equation

7x + 3y = 8

7 [ ( -25 + 4y )/5 ] + 3y = 8

[ ( -25*7 ) + ( 4y*7 )/5 ] + 3y = 8

( -175 + 28y )/5 + 3y = 8

( -175/5 ) + ( 28y/5 ) + 3y = 8

-35 + 28y/5 + 3y = 8

28y/5 + 3y = 8 + 35

28y/5 + 3y = 43

( 28y/5 + 3y ) 5 = 43 ( 5 )

28y + 15y = 215

43y = 215

y = 5

x = ( -25 + 4y )/5

x = [ -25 + ( 4 * 5 ) ]/5

x = ( -25 + 20 )/5

x = ( -5 )/5

x = -1

( -1, 5 )