contestada

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)

Respuesta :

calculista

Answer:

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)            

Step-by-step explanation:

Part 1) we have

[tex]2x-6y=10[/tex] ----> equation A

[tex]x+8y=5[/tex] ---> equation B

Solve the system by elimination

Multiply equation B by -2 both sides

[tex]-2(x+8y)=-2(5)[/tex]

[tex]-2x-16y=-10[/tex] ----> equation C

Adds equation A and equation C

[tex]2x-6y=10\\-2x-16y=-10\\--------\\-6y-16y=10-10\\-22y=0\\y=0[/tex]

Find the value of x

substitute the value of y in any equation

[tex]x+8(0)=5[/tex]

[tex]x=5[/tex]

therefore

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

Part 2) we have

[tex]3x-y=-5[/tex] ----> [tex]y=3x+5[/tex] ----> equation A

[tex]x+4y=7[/tex] ---> equation B

Solve the system by substitution

substitute equation A in equation B

[tex]x+4(3x+5)=7[/tex]

solve for x

[tex]x+12x+20=7[/tex]

[tex]13x=7-20[/tex]

[tex]13x=-13[/tex]

[tex]x=-1[/tex]

Find the value of y

[tex]y=3(-1)+5=2[/tex]

therefore

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

Part 3) we have

[tex]2x-2y=12[/tex] ----> equation A

[tex]-2x-3y=-22[/tex] ---> equation B

Solve the system by elimination

Adds equation A and equation B

[tex]2x-2y=12\\-2x-3y=-22\\--------\\-2y-3y=12-22\\-5y=-10\\y=2[/tex]

Find the value of x

substitute the value of y in any equation

[tex]2x-2(2)=12[/tex]

[tex]2x-4=12[/tex]

[tex]2x=12+4[/tex]

[tex]2x=16[/tex]

[tex]x=8[/tex]

therefore

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

Part 4) we have

[tex]x-y=2[/tex] ----> [tex]y=x-2[/tex] ----> equation A

[tex]2x+y=13[/tex] ---> equation B

Solve the system by substitution

substitute equation A in equation B

[tex]2x+x-2=13[/tex]

solve for x

[tex]3x=13+2[/tex]

[tex]3x=15[/tex]

[tex]x=5[/tex]

Find the value of y

[tex]y=5-2=3[/tex]

therefore

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

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