Question

1.) Solve the following system of equations.

Answer 1

Answer:

Part 1) No solutions

Part 2) $y=9$

part 3) $(0,-3)$

Step-by-step explanation:

Part 1) we have

$3x-2y=6$ -------> equation A

$6x-4y=14$ -------> equation B

Multiply the equation A by $2$

$2(3x-2y)=2*6$ --------> $6x-4y=12$

Equation A and equation B represent parallel lines

therefore

Is a inconsistent system of equations

The system has no solution

Part 2) we have

$5x+4y=1$ -------> equation A

$4x+3y=-1$ -------> equation B

Multiply equation A by $4$

$4*(5x+4y)=4*1$ ------> $20x+16y=4$ ------> equation C

Multiply equation B by $-5$

$-5*(4x+3y)=-5*-1$ ------> $-20x-15y=5$ ------> equation D

Adds equation C and equation D

$20x+16y=4\\-20x-15y=5\\---------\\16y-15y=4+5\\y=9$

Part 3) we have

$y< 2x+4$ -------> inequality A

$y< -2x+2$ -------> 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) $(1,0)$

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

Verify inequality A

$0< 2(1)+4$

$0< 6$ -------> is true

Verify inequality B

$0< -2(1)+2$

$0< 0$  ------> is not true

the point $(1,0)$ is not a solution

case B) $(-5,-2)$

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

Verify inequality A

$-2< 2(-5)+4$

$-2< -6$ -------> is not true

the point $(-5,-2)$ is not a solution

case C) $(0,-3)$

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

Verify inequality A

$-3< 2(0)+4$

$-3< 4$ -------> is true

Verify inequality B

$-3< -2(0)+2$

$-3< 2$  ------> is true

the point $(0,-3)$ is a solution

case D) $(-1,5)$

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

Verify inequality A

$5< 2(-1)+4$

$5< 2$ -------> is not true

the point $(-1,5)$ is not a solution

Answer 2

1- no solution
2- 7
3-