Question

4. Solve the system of equations. (6 points)2x-3y = 21-5x+2y = ?a.) Explain the steps you would take to solve the system by eliminating the x-termsb.) Explain the steps you would take to solve the system by eliminating the y-termsc.) Choose either of the methods described in a or b to solve the system of equations. Write your answer as an ordered pair. Show your work.

Answer 1

We have the following system of equations given:

2x - 3y = 21 (1)

-6x +2y = 7 (2)

Part a

We can multiple the first equation by 3 and we can add the result to equation (2) and we have:

6x -9y = 63

-6x +2y =7

____________

-7y = 70

y= 70/-7 = -10

Part b

We can multiply the first equation by 2/3 and we can add the result to the second equation and we got:

4/3x - 2y = 14

-6x +2y= 7

____________

-14/3 x = 21

x= -9/2 = -4.5

Part c

We can use other methods for example substitution in order to solve the problem. For example we can solve for x in the first equation and we have:

`x=(21+3y)/(2)`

And replacing in the second one we got:

`-5((21+3y)/(2))+2y=7`

And after solve for x and y we got:

x= -9/2

y = -10