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1.) Solve the following system of equations.

3x - 2y = 6
6x - 4y = 14

A.) (0, 0)
B.) (6, 14)
C.) Infinitely Many Solutions
D.) 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

A.) -7
B.) 7
C.) 9
D.) -9

3.) Which point lies in the solution set for the following system of inequalities?

A.) y < 2x + 4
B.) y < -2x + 2
C.) (1, 0)
D.) (-5, -2)
E.) (0, -3)
F.) (-1, 5)

Respuesta :

calculista

Answer:

Part 1) option D) No solutions

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

Part 3) option E [tex]E(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

Divide the equation B by [tex]2[/tex] both sides

[tex]6x-4y=14[/tex] --------> [tex]3x-2y=7[/tex]

Equation A and equation B represent a parallel lines, because their have the same slope [tex]m=\frac{3}{2}[/tex]

therefore

The system of equation does not have solution

Part 2) we have  

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

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

Multiply the equation A by [tex]4[/tex] both sides

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

Multiply the equation B by [tex]-5[/tex] both sides

[tex]4x+3y=-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 point lie in the solution set of the system of inequalities, then the point must be satisfy the inequalities of the system

a) point [tex]C(1,0)[/tex]

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

therefore

the point  [tex]C(1,0)[/tex] does not lie in the solution set of the system of inequalities

b) point [tex]D(-5,-2)[/tex]

Verify inequality A

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

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

therefore

the point   [tex]D(-5,-2)[/tex] does not lie in the solution set of the system of inequalities

c) point [tex]E(0,-3)[/tex]

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

therefore

the point [tex]E(0,-3)[/tex] lies in the solution set of the system of inequalities

d) point [tex]F(-1,5)[/tex]

Verify inequality A

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

[tex]5<2[/tex]  -------> is not true

therefore

the point [tex]F(-1,5)[/tex] does not lie in the solution set of the system of inequalities

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