Question

Equation 1: 8x+2y=308x+2y=30

Equation 2: 7x+2y=247x+2y=24


Which variable pair should we try to eliminate?



The x's because the coefficients are the same.


The y's because the coefficients are the same.


The x's because the coefficients are different?


The y's because the coefficients are different?

Now that we've eliminated the variable pair, what is the resulting equation?



15y+4y=5415y+4y=54

x+4y=54x+4y=54

4y=64y=6

Consider the following system of equations:



Equation 1: 8x+2y=308x+2y=30
Equation 2: 7x+2y=247x+2y=24


What is the solution to the system?



(6,8)

(6,-9)

(1,11)

(0,12)

Answer 1

Part a) We should try to eliminate the y's because the coefficients are the same

Part b) The solution is the point (6,-9)

Explanation:

Part a) Which variable pair should we try to eliminate?

we have

`8x+2y=30` ----> equation 1

`7x+2y=24` ----> equation 2

Solve by elimination

We should try to eliminate the y's because the coefficients are the same

Part b) What is the solution to the system?

Multiply equation 2 by -1 both sides

`-1(7x+2y)=-1(24)`

`-7x-2y=-24` -----> equation 3

Adds equation 1 and equation 3

`8x+2y=30\\-7x-2y=-24\\-------\\8x-7x=30-24\\x=6`

Find the value of y

`8x+2y=30[/tex</p><p>[tex]8(6)+2y=30`

`2y=30-48`

`y=-9`

The solution is the point (6,-9)