1. solve the system by elimination. 2.solve the system by substitution.

Step One

Add the first and third

-2x + 2y + 3z = 0

2x + 3y + 3z = 5

        5y + 6z = 5

Step Two

Add the second and third together.

- 2x - y + z = -3

2x + 3y + 3z = 5

       2y + 4z = 2            Divide this result by 2

         y + 2z = 1             multiply this result by 5

        5y + 10z = 5

Step three

Subtract the result of step 2 from the result of step one

         5y + 10z = 5

         5y +  6z = 5        Subtract

                  4z = 0

                    z = 0

Step Four

Solve for y

5y + 6z = 5     But z = 0

5y = 5

y = 1

Step Four

Solve for x . Use equation 3 in the givens.

2x + 3y + 3z = 5

2x + 3*1) + 3*0 = 5

2x = 5 - 3

2x = 2

x = 1

Answer

x = 1

y = 1

z =0       This has been checked and found to be correct.

Problem 2

Substitution is not the best way to do this. Divide the last equation by 2 and add it to the first one.

Step One

divide equation 3 by 2.

x + z = 2

Step Two

Add step one to equation 1

-x - y - z = - 8

x    +    z =  2

    - y = - 6

      y =   6

Step Three

Put this result into equation 1.

-x - 6 - z = - 8

-x - z = - 2

x + z = 2     Multiply this equation by 4

4x + 4z = 8

Step four

Put y = 7 into the second equation.

-4x + 4y + 5z =  7

-4x + 4*6 + 5z = 7

-4x + 24 + 5z = 7

-4x          +5z = -17

Step 5

Add the results from Step 3 and Step 4 together.

-4x + 5z = - 17

4x + 4z = 8

9z = - 9

z = - 1

Step 6

Find x

-x - y - z = - 8

-x -6 + 1 =- 8

-x - 5 = - 8

-x = - 3

x = 3      

Answers

x = 3

y = 6

z = -1    verified to be correct.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

jml angle lkj & angle mj = lm