Match the system of equations to their solutions

x=2, y=7 > y=11-2x  and 4x-3y=-13

x=5, y=2 > 2x+y=12 and x=9-2y

x=3, y=5  > 2x+y=11 and x-2y=-7

x=7, y=3 > x+3y=16  and  2x-y=11

Step-by-step explanation:

Part 1) we have

2x+y=12 > equation A

x=9-2y > equation B

Solve by substitution

Substitute equation B in equation A and solve for y

2(9-2y)+y=12

18-4y+y=12

4y-y=18-12

3y=6

y=2

Find the value of x

x=9-2(2)=5

therefore

The solution is

x=5, y=2

Part 2) we have

x+2y=9 > equation A

2x+4y=20 ---> equation B

Multiply equation A by 2 both sides

2(x+2y)=9*2

2x+4y=18 > equation C

Compare equation C with equation B

Both equations have the same slope with different y-intercept

therefore

The lines are parallel and the system has no solution

Part 3) we have

x+3y=16 > equation A

2x-y=11 > equation B

Solve the system by elimination

Multiply equation B by 3 both sides

3(2x-y)=11*3

6x-3y=33 > equation C

Adds equation A and equation C

x+3y=16

6x-3y=33

x+6x=16+33

7x=49

x=7

Find the value of y

x+3y=16

7+3y=16

3y=16-7

3y=9

y=3

therefore

The solution is

x=7, y=3

Part 4) we have

y=11-2x > equation A

4x-3y=-13 ---> equation B

Solve by substitution

Substitute equation A in equation B and solve for x

4x-3(11-2x)=-13

4x-33+6x=-13

10x=-13+33

10x=20

x=2

Find the value of y

y=11-2(2)=7

therefore

The solution is

x=2, y=7

Part 5) we have

y=10+x > equation A

-3x+3y=30 ---> equation B

Multiply equation A by 3 both sides

3*y=3*(10+x)

3y=30+3x

Rewrite

-3x+3y=30 > equation C

equation B and equation C are identical

therefore

The system has infinitely solutions

Part 6) we have

2x+y=11 > equation A

x-2y=-7 > equation B

Solve by elimination

Multiply equation A by 2 both sides

2(2x+y)=11*2

4x+2y=22 > equation C

Adds equation B and equation C and solve for x

x-2y=-7

4x+2y=22

x+4x=-7+22

5x=15

x=3

Find the value of y

x-2y=-7

3-2y=-7

2y=3+7

2y=10

y=5

therefore

The solution is

x=3, y=5  

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step-by-step explanation: