4. solve the system of equations.
2x-3y=21
-6x+2y=7
part i: explain the steps you would take to solve the system by eliminating the x-terms.
part ii: explain the steps you would take to solve the system by eliminating the y-terms.
part iii: choose either of the methods described in parts i or ii to solve the system of equations. write your answer as an ordered pair. show your work.

Part I : Eliminating x terms

Step 1: There are two equations. To eliminate the x terms we have to make similar x-terms in both the equation.

Step 2: Cancel x- terms by using addition or subtraction of 2 equations.

Step 3: Find the value of y and substitute into any equation and find the value of y

Part II : Eliminating y terms

Step 1: There are two equations. To eliminate the y terms we have to make similar y-terms in both the equation.

Step 2: Cancel y- terms by using addition or subtraction of 2 equations.

Step 3: Find the value of x and substitute into any equation and find the value of x

The value of (x,y) = (-4.5, -10)

Step-by-step explanation:

It is given that,

2x-3y=21   (1)

-6x+2y=7  (2)

To find the value of x and y

Eliminating x terms:-

(1) ⇒ 2x-3y = 21

(1) * 3 ⇒ 6x - 9y  = 63  (3)

Adding eq(2) and eq(3)

-6x + 2y =   7  (2)

6x - 9y  = 63  (3)

       -7y = 70

y = 70/-7 = -10

Substituting the value of y in eq(1)

eq(1) ⇒2x - 3y = 21

2x - 3 *(-10) = 21

2x + 30 = 21

2x = 21 - 30 = -9

x = -9/2 = -4.5

Therefore the value of (x,y) = (-4.5, -10)