Solves a systems of linear equations in two variables. Solve the following systems by graphing
1) 2x + y = 5 and x-3y = - 8
2) 6x - 3y = - 9 and 2x + 2y = -6

Solve the following systems by substitution
3) y = 5x-3 and -x - 5y = - 11
4) 2x - 6y = 24 and x - 5y - 22

Solve the following systems by elimination
5) - 4x - 2y = -2 and 4x + 8y = -24
6) x - y = 11 and 2x + y = 19

Linear equations are represented by straight lines.

Graphs

(1) 2x + y = 5 and x - 3y = -8

See attachment for the graphs of 2x + y = 5 and x - 3y = -8

From the graph, we have:

(x,y) = (1,3)

(2) 6x - 3y =  -9 and 2x + 2y = -6

See attachment for the graphs of 6x - 3y =  -9 and 2x + 2y = -6

From the graph, we have:

(x,y) = (-2,-1)

Substitution

3) y = 5x-3 and -x - 5y = - 11

Make x the subject in

Substitute in

Open bracket

Collect like terms

Divide both sides by 2

Substitute in

So, the solution is (x,y) = (1,2)

4) 2x - 6y = 24 and x - 5y = 22

Make x the subject in

Substitute in

Collect like terms

Divide by 4

Substitute in

So, the solution is (x,y) = (-3,-5)

Elimination

5) - 4x - 2y = -2 and 4x + 8y = -24

Add both equations to eliminate x

Divide both sides by 6

Substitute in

Collect like terms

Divide both sides by 4

Hence, the solution is (x,y) = (8/3,-13/3)

6) x - y = 11 and 2x + y = 19

Add both equations to eliminate y

Divide through by 3

Substitute in

Collect like terms

Hence, the solution is (x,y) = (10,-1)

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1) x = 1, y = 3

2) x = -2, y = -1

3) x = 1, y = 2

4) x = 63, y = 17

5) x = 1 , y = 4

6) x = 10, y = -1

Step-by-step explanation:

1 and 2 require graphing so if you graph out both equations and find their intersection, the point on the x-axis that intersected is the value of x and the point on the y-axis that intersected is the value of y. I have attached the pictures of the graphs.

3) I will be substituting y = 5x-3 into -x-5y = -11

-x-5y = -11

-x-5(5x-3) = -11

-x-25x+15 = -11

-26x+15 = -11

-26x = -11-15

-26x = -26

x = -26 ÷ -26

x = 1

Substitute x = 1 into y = 5x-3

y = 5x-3

y = 5(1)-3

y = 5-3

y = 2

4) I will substitute x into 2x-6y=24

x = -22+5y

2x-6y = 24

2(-22+5y)-6y = 24

-44+10y-6y = 24

4y = 24+44

4y = 68

y = 68 ÷ 4

y = 17

Substitute y = 17 into 2x-6y=24

2x-6y=24

2x-6(17) = 24

2x-102  =24

2x = 24 + 102

2x = 126

x = 126 ÷ 2

x = 63

5) I will eliminate 4x.

4x+8y-4x-2y = -2-24

6y = 26

y = 26 ÷ 6

y = 4

Substitute y = 4 into - 4x - 2y = -2

-4x-2y = -2

-4x-2(4) = -2

-4x-8 = -2

-4x = -2+ 8

-4x = 6

x = 6 ÷ -4

x = 1

6) We will eliminate y.

2x+y+x-y = 19+11

3x = 30

x = 30 ÷ 3

x = 10

Subsitute x = 10 into x-y=11

x-y = 11

10-y = 11

-y = 11-10

-y = 1

y = -1

the barter

answer: idk

step-by-step explanation: