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1.) Solve the following system of equations.
3x - 2y = 6
6x - 4y = 14

(0, 0)
(6, 14)
Infinitely Many Solutions
No Solutions

2.) What is the value of the y variable in the solution to the following system of equations?
5x + 4y = 1
4x + 3y = -1

-7
7
9
-9

3.) Which point lies in the solution set for the following system of inequalities?
y < 2x + 4
y < -2x + 2

(1, 0)
(-5, -2)
(0, -3)
(-1, 5)

Respuesta :

calculista

Answer:

Part 1) No solutions

Part 2) [tex]y=9[/tex]

part 3) [tex](0,-3)[/tex]

Step-by-step explanation:

Part 1) we have

[tex]3x-2y=6[/tex] -------> equation A

[tex]6x-4y=14[/tex] -------> equation B

Multiply the equation A by [tex]2[/tex]

[tex]2(3x-2y)=2*6[/tex] --------> [tex]6x-4y=12[/tex]

Equation A and equation B represent parallel lines

therefore

Is a inconsistent system of equations

The system has no solution

Part 2) we have

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

[tex]4x+3y=-1[/tex] -------> equation B

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

[tex]4*(5x+4y)=4*1[/tex] ------> [tex]20x+16y=4[/tex] ------> equation C

Multiply equation B by [tex]-5[/tex]

[tex]-5*(4x+3y)=-5*-1[/tex] ------> [tex]-20x-15y=5[/tex] ------> equation D

Adds equation C and equation D

[tex]20x+16y=4\\-20x-15y=5\\---------\\16y-15y=4+5\\y=9[/tex]

Part 3) we have

[tex]y< 2x+4[/tex] -------> inequality A

[tex]y< -2x+2[/tex] -------> inequality B

we know that

If a ordered pair lie in the solution set of the system of inequalities

then

the ordered pair must be satisfy the system of inequalities

case A) [tex](1,0)[/tex]

substitute the value of x and the value of y in both inequalities

Verify inequality A

[tex]0< 2(1)+4[/tex]

[tex]0< 6[/tex] -------> is true

Verify inequality B

[tex]0< -2(1)+2[/tex]

[tex]0< 0[/tex]  ------> is not true

the point [tex](1,0)[/tex] is not a solution

case B) [tex](-5,-2)[/tex]

substitute the value of x and the value of y in both inequalities

Verify inequality A

[tex]-2< 2(-5)+4[/tex]

[tex]-2< -6[/tex] -------> is not true

the point [tex](-5,-2)[/tex] is not a solution

case C) [tex](0,-3)[/tex]

substitute the value of x and the value of y in both inequalities

Verify inequality A

[tex]-3< 2(0)+4[/tex]

[tex]-3< 4[/tex] -------> is true

Verify inequality B

[tex]-3< -2(0)+2[/tex]

[tex]-3< 2[/tex]  ------> is true

the point [tex](0,-3)[/tex] is a solution

case D) [tex](-1,5)[/tex]

substitute the value of x and the value of y in both inequalities

Verify inequality A

[tex]5< 2(-1)+4[/tex]

[tex]5< 2[/tex] -------> is not true

the point [tex](-1,5)[/tex] is not a solution

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