Question

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.

Answer 1

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)

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)