5x + y = 9

3x + 2y = 4

Solve with elimination method

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5x + y = 93x + 2y = 4Solve with elimination method

5x + y = 9

3x + 2y = 4

Solve with elimination method

x=2 y=-1

Step-by-step explanation:

multiply the top equation by negative 2. then it is -7=-14

then you dive and find out that x=2 and plug it inot the equation and solve for x 10+?=9 which is -1

See attached picture for the answers:

[tex]1. solve the system by graphing. { -2x = 2y - 4 { 2x - y = -5 2. without graphing, is the system i[/tex]

x=2

y=-1

Step-by-step explanation:

make it so that you can cancel out the y

to do this multiply the top equation by 2

10x+2y=18

3x+2y=4

subtract to get rid of 2y

7x=14

x=2

substitute the x into one equation

3(2)+2y=4

6+2y=4

2y=-2

y=-1

i haven’t learned this yet but you should find the solutions of each one and put them as an ordered pair

2. x + y = 82

x - y = 24

add

2x = 106

x = 53

x + y = 82

53 + y = 82

y = 82 - 53

y = 29

solution is : (53,29)

3. y = 2x

y = 4x + 6

2x = 4x + 6

2x - 4x = 6

-2x = 6

x = -3

y = 2x

y = 2(-3)

y = -6

solution is (-3,-6)

4. 5x + 8y = -29

7x - 2y = -67...multiply by 4

5x + 8y = -29

28x - 8y = - 268 ..result of multiplying by 4

add

33x = - 297

x = - 9

5x + 8y = -29

5(-9) + 8y = -29

-45 + 8y = -29

8y = -29 + 45

8y = 16

y = 2

solution is : (-9,2)

5. y = -4x + 6

y = -5x - 4

-4x + 6 = -5x - 4

-4x + 5x = -4 - 6

x = -10

y = -4x + 6

y = -4(-10) + 6

y = 40 + 6

y = 46

solution is (-10,46)

6. H(m) = 2m + 12

H(m) = 3m + 10

7. -8x + 4y > -52

4y > 8x - 52

y > 2x - 13 <==

8. 3x - y = 28

3x + y = 14

add

6x = 42

x = 7

3x - y = 28

3(7) - y = 28

21 - y = 28

-y = 28 - 21

-y = 7

y = -7

solution is (7,-7)

10. 5x - 5y > 70

-5y > -5x + 70

y < x - 14 <==

11. sorry...dont know

12. y = 4x + 4

y = -3x - 3

4x + 4 = -3x - 3

4x + 3x = -3 - 4

7x = -7

x = -1

y = 4x + 4

y = 4(-1) + 4

y = 0

solution is (-1,0)

13. -12x - 2y > - 42

-2y > 12x - 42

y < -6x + 21 <==

14. -5x + 2y = 9

3x + 5y = 7

solution is (-1,2)

15. 3x + 6y = -2

15x + 30y = -10divide by 5 to reduce = 3x + 6y = -2

is the same lineinfinite solutions

1. (the graph)y < = 3x - 43rd one

9. (2nd graph)y < = -3x + 4last one

Part 1) Solve the system by graphing.

we have

[tex]-2x = 2y - 4\\2x - y = -5[/tex]

using a graph tool

see the attached figure N 1

the solution is the point [tex](-1,3)[/tex]

therefore

the answer part 1) is

[tex](-1,3)[/tex]

Part 2) Without graphing, is the system independent, dependent, inconsistent? [tex]y =2x-8[/tex] -------> equation [tex]1[/tex]

[tex]2x - y=8[/tex] -------> equation [tex]2[/tex]

Multiply equation [tex]1[/tex] by [tex]-1[/tex]

[tex]-y =-2x+8[/tex]-------> [tex]2x-y=8[/tex]

so

equation [tex]1[/tex] is equal to equation [tex]2[/tex]

therefore

The system has no solution, is a inconsistent system

the answer part 2) is the option

C. Inconsistent

Part 3) What is the solution of the following system?

[tex]-2x - y = 1 \\-4x - 2y =-1[/tex]

the lines are parallel

so

The system has an infinite number of solutions, it is dependent

therefore

the answer Part 3) is the option

A. Infinitely many solutions

Part 4) Solve the system of inequalities by graphing.

[tex]y \leq-4x - 1\\y 3x - 1[/tex]

using a graph tool

see the attached figure N 2

The solution is the shaded area

therefore

the answer part 4) in the attached figure N 2

Part 5) Your club is baking strawberry and apple pies for a bake sale. They need at most 18 pies, and cannot have more than 12 apple pies. Write and graph a system of inequalities to model this system

Let

x -------> the number of strawberry pies

y -------> the number of apples pies

we know that

[tex]x+y\leq 18[/tex]

[tex]y\leq12[/tex]

using a graph tool

see the attached figure N 3

the solution is the shaded area

therefore

the answer Part 5) is the option

B. { x is more than or equal to 0

{ y is more than or equal to 0

{ x + y is less than or equal to 18

{ y is less than or equal to 12

Part 6) A rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. Another agency charges a fee of $70.00 plus $54.00 per day to rent the same car.

Using a graphing calculator, to find the number of days for which the costs are the same. Round your answer to the nearest whole day

Let

x-------> the number of days

y-------> total cost to rent a car

we know that

First agency

[tex]y=110+46x[/tex] --------> equation [tex]1[/tex]

Second agency

[tex]y=70+54x[/tex] --------> equation [tex]2[/tex]

so

to find the number of days for which the costs are the same solve the system of equations

the intersection both graphs is the solution

using a graph tool

see the attached figure N 4

the solution is the point [tex](5,340)[/tex]

therefore

the answer is

[tex]5\ days[/tex]

Part 7) Solve the system by substitution.

[tex]-4.5x-2y =-12.5[/tex] --------> equation [tex]1[/tex]

[tex]3.25x- y=-0.75[/tex]

[tex]y=3.25x+0.75[/tex] --------> equation [tex]2[/tex]

Substitute equation [tex]2[/tex] in equation [tex]1[/tex]

[tex]-4.5x-2*[3.25x+0.75]=-12.5[/tex]

[tex]-4.5x-6.50x-1.50=-12.5[/tex]

[tex]-11x=-12.5+1.50[/tex]

[tex]-11x=-11[/tex]

[tex]x=1[/tex]

find the value of y

[tex]y=3.25*1+0.75[/tex]

[tex]y=4[/tex]

therefore

the answer part 7) is

the solution is the point [tex](1,4)[/tex]

Part 8) Solve the system using elimination.

[tex]5x+4y=12[/tex] ------> equation [tex]1[/tex]

[tex]3x-3y=18[/tex] ------> equation [tex]2[/tex]

Multiply equation [tex]1[/tex] by [tex]3[/tex]

[tex]15x+12y=36[/tex] ------> equation [tex]3[/tex]

Multiply equation [tex]2[/tex] by [tex]4[/tex]

[tex]12x-12y=72[/tex] ------> equation [tex]4[/tex]

Add equation [tex]3[/tex] and equation [tex]4[/tex]

[tex]15x+12y=36\\12x-12y=72\\-------\\27x+0y=108\\x=108/27\\ x= 4[/tex]

Find the value of y

[tex]5*4+4y=12[/tex]

[tex]4y=12-20[/tex]

[tex]y=-8/4[/tex]

[tex]y=-2[/tex]

therefore

the answer Part 8) is

the solution is the point [tex](4,-2)[/tex]

Part 9) The length of a rectangle is 9.7 cm more than 4 times the width. If the perimeter of the rectangle is 91.4 cm, what are it's dimensions?

Let

x-------> the length of the rectangle

y-------> the width of the rectangle

we know that

the perimeter of the rectangle is equal to

[tex]P=2x+2y\\ P=91.4\ cm[/tex]

so

[tex]2x+2y=91.4[/tex]

Divide by [tex]2[/tex] both sides

[tex]x+y=45.7[/tex] -------> equation [tex]1[/tex]

[tex]x=9.7+4y[/tex] -------> equation [tex]2[/tex]

substitute equation [tex]2[/tex] in equation [tex]1[/tex]

[tex](9.7+4y)+y=45.7[/tex]

[tex]5y=45.7-9.7[/tex]

[tex]5y=36[/tex]

[tex]y=7.2\ cm[/tex]

find the value of x

[tex]x=9.7+4*7.2[/tex]

[tex]x=38.5\ cm[/tex]

therefore

the answer part 9) is

the length of the rectangle is [tex]38.5\ cm[/tex]

the width of the rectangle is [tex]7.2\ cm[/tex]

[tex]1. solve the system by graphing. { -2x = 2y - 4 { 2x - y = -5 2. without graphing, is the system i[/tex][tex]1. solve the system by graphing. { -2x = 2y - 4 { 2x - y = -5 2. without graphing, is the system i[/tex]

[tex]1. solve the system by graphing. { -2x = 2y - 4 { 2x - y = -5 2. without graphing, is the system i[/tex]

[tex]1. solve the system by graphing. { -2x = 2y - 4 { 2x - y = -5 2. without graphing, is the system i[/tex]