Question

Solve each system. Then drag each one to the column headed by a point which could be its solution.

2x-6y=10
x+8y=5

3x-y=-5
x+4y=7

2x-2y=12
-2x-3y=-22

x-y=2
2x+y=13

(5,y) (x,2)

Answer 1

Part 1) The solution of the system of equations is the point (5,0) -> the solution could be (5,y)

Part 2) The solution of the system of equations is the point (-1,2) --> the solution could be (x,2)

Part 3) The solution of the system of equations is the point (8,2) -> the solution could be (x,2)

Part 4) The solution of the system of equations is the point (5,3) -> the solution could be (5,y)

Explanation:

Part 1) we have

`2x-6y=10` ----> equation A

`x+8y=5` ---> equation B

Solve the system by elimination

Multiply equation B by -2 both sides

`-2(x+8y)=-2(5)`

`-2x-16y=-10` ----> equation C

Adds equation A and equation C

`2x-6y=10\\-2x-16y=-10\\--------\\-6y-16y=10-10\\-22y=0\\y=0`

Find the value of x

substitute the value of y in any equation

`x+8(0)=5`

`x=5`

therefore

The solution of the system of equations is the point (5,0) -> the solution could be (5,y)

Part 2) we have

`3x-y=-5` ---->
`y=3x+5` ----> equation A

`x+4y=7` ---> equation B

Solve the system by substitution

substitute equation A in equation B

`x+4(3x+5)=7`

solve for x

`x+12x+20=7`

`13x=7-20`

`13x=-13`

`x=-1`

Find the value of y

`y=3(-1)+5=2`

therefore

The solution of the system of equations is the point (-1,2) --> the solution could be (x,2)

Part 3) we have

`2x-2y=12` ----> equation A

`-2x-3y=-22` ---> equation B

Solve the system by elimination

Adds equation A and equation B

`2x-2y=12\\-2x-3y=-22\\--------\\-2y-3y=12-22\\-5y=-10\\y=2`

Find the value of x

substitute the value of y in any equation

`2x-2(2)=12`

`2x-4=12`

`2x=12+4`

`2x=16`

`x=8`

therefore

The solution of the system of equations is the point (8,2) -> the solution could be (x,2)

Part 4) we have

`x-y=2` ---->
`y=x-2` ----> equation A

`2x+y=13` ---> equation B

Solve the system by substitution

substitute equation A in equation B

`2x+x-2=13`

solve for x

`3x=13+2`

`3x=15`

`x=5`

Find the value of y

`y=5-2=3`

therefore

The solution of the system of equations is the point (5,3) -> the solution could be (5,y)