Match the systems of linear equations with their solutions.

The solutions of linear equations in the procedure

Step-by-step explanation:

Part 1) we have

x+y=-1 > equation A

-6x+2y=14 > equation B

Solve the system by elimination

Multiply the equation A by 6 both sides

6*(x+y)=-1*6

6x+6y=-6 > equation C

Adds equation C and equation B

6x+6y=-6

-6x+2y=14

6y+2y=-6+14

8y=8

y=1

Find the value of x

substitute in the equation A

x+y=-1 > x+1=-1 > x=-2

The solution is the point (-2,1)

Part 2) we have

-4x+y=-9 > equation A

5x+2y=3 > equation B

Solve the system by elimination

Multiply the equation A by -2 both sides

-2*(-4x+y)=-9*(-2)

8x-2y=18 > equation C

Adds equation B and equation C

5x+2y=3

8x-2y=18

5x+8x=3+18

13x=21

x=21/13

Find the value of y

substitute in the equation A

-4x+y=-9 > -4(21/13)+y=-9 > y=-9+84/13 > y=-33/13

The solution is the point (21/13,-33/13)

Part 3) we have

-x+2y=4 > equation A

-3x+6y=11 > equation B

Multiply the equation A by 3 both sides

3*(-x+2y)=4*3 > -3x+6y=12

so

Line A and Line B are parallel lines with different y-intercept

therefore

The system has no solution

Part 4) we have

x-2y=-5 > equation A

5x+3y=27 > equation B

Solve the system by elimination

Multiply the equation A by -5 both sides

-5*(x-2y)=-5*(-5)

-5x+10y=25 > equation C

Adds equation B and equation C

5x+3y=27

-5x+10y=25

3y+10y=27+25

13y=52

y=4

Find the value of x

Substitute in the equation A

x-2y=-5 > x-2(4)=-5 > x=-5+8 > x=3

The solution is the point (3,4)

Part 5) we have

6x+3y=-6 > equation A

2x+y=-2 > equation B

Multiply the equation B by 3 both sides

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

6x+3y=6

so

Line A and Line B is the same line

therefore

The system has infinite solutions

Part 6) we have

-7x+y=1 > equation A

14x-7y=28 > equation B

Solve the system by elimination

Multiply the equation A by 7 both sides

7*(-7x+y)=1*7

-49x+7y=7 > equation C

Adds equation B and equation C

14x-7y=28

-49x+7y=7

14x-49x=28+7

-35x=35

x=-1

Find the value of y

substitute in the equation A

-7x+y=1  > -7(-1)+y=1 > y=1-7 > y=-6

The solution is the point (-1,-6)