Mathematics, 06.12.2020 14:00 neazisa

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

Answers: 2

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Answer from: ari9843

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 $\mathbf{-x - 5y = -11}$

$\mathbf{x= 11 - 5y}$

Substitute $\mathbf{x= 11 - 5y}$ in $\mathbf{y = 5x - 3}$

$\mathbf{y = 5(11 - 5y) - 3}$

Open bracket

$\mathbf{y = 55 - 25y - 3}$

Collect like terms

$\mathbf{y +25y= 55 - 3}$

$\mathbf{26y= 52}$

Divide both sides by 2

$\mathbf{y= 2}$

Substitute $\mathbf{y= 2}$ in $\mathbf{x= 11 - 5y}$

$\mathbf{x =11 - 5(2)}$

$\mathbf{x =1}$

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

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

Make x the subject in $\mathbf{x - 5y = 22}$

$\mathbf{x = 5y + 22}$

Substitute $\mathbf{x = 5y + 22}$ in $\mathbf{2x - 6y =24}$

$\mathbf{2(5y + 22) - 6y =24}$

$\mathbf{10y + 44 - 6y =24}$

Collect like terms

$\mathbf{10y - 6y =24 - 44}$

$\mathbf{4y =- 20}$

Divide by 4

$\mathbf{y =- 5}$

Substitute $\mathbf{y =- 5}$ in $\mathbf{x = 5y + 22}$

$\mathbf{x = 5(-5) + 22}$

$\mathbf{x = -3}$

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

Elimination

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

Add both equations to eliminate x

$\mathbf{-4x + 4x - 2y + 8y = -2- 24}$

$\mathbf{6y = -26}$

Divide both sides by 6

$\mathbf{y = -\frac{13}{3}}$

Substitute $\mathbf{y = -\frac{13}{3}}$ in $\mathbf{4x + 8y = -24}$

$\mathbf{4x - 8 \times \frac{13}{3} = -24}$

$\mathbf{4x - \frac{104}{3} = -24}$

Collect like terms

$\mathbf{4x = \frac{104}{3} -24}$

$\mathbf{4x = \frac{104-72}{3} }$

$\mathbf{4x = \frac{32}{3} }$

Divide both sides by 4

$\mathbf{x = \frac{8}{3} }$

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

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

Add both equations to eliminate y

$\mathbf{x + 2x - y + y = 11 +19}$

$\mathbf{3x = 30}$

Divide through by 3

$\mathbf{x = 10}$

Substitute $\mathbf{x = 10}$ in $\mathbf{x - y = 11}$

$\mathbf{10 - y = 11}$

Collect like terms

$\mathbf{ y =10 - 11}$

$\mathbf{ y =- 1}$

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

Read more about linear equations at:

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Solves a systems of linear equations in two variables.

Solve the following systems by graphing1) 2x

Answer from: sierravick123owr441

1) x = 1, y = 3

2) x = -2, y = -1

3) x = 1, y = 2

4) x = 63, y = 17

5) x = 1 $\frac{2}{3}$ , y = 4 $\frac{1}{3}$

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 $\frac{1}{3}$

Substitute y = 4 $\frac{1}{3}$ into - 4x - 2y = -2

-4x-2y = -2

-4x-2(4 $\frac{1}{3}$ ) = -2

-4x-8 $\frac{2}{3}$ = -2

-4x = -2+ 8 $\frac{2}{3}$

-4x = 6 $\frac{2}{3}$

x = 6 $\frac{2}{3}$ ÷ -4

x = 1 $\frac{2}{3}$

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

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Solves a systems of linear equations in two variables. Solve the following systems by graphing

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