Question

Use elimination to solve the system of equations

Answer 1

Solution:

There are Infinitely many solutions.

Explanation:

We have been given the system of equations

$3x+2y=7.......(1)\\\\-9x-6y=-21......(2)$

In elimination method, we multiply any of the equation by some constant and then add/subtract the equations to eliminate any variable x or y.

Let us multiply equation 1 by 3

$9x+6y=21.......(3)\\\\-9x-6y=-21......(4)$

Add equations 3 and 4, we get

$9x-9x+6y-6y=21-21\\\\0=0$

We got 0=0, which is always true.

Hence, there are Infinitely many solutions.

C is the correct option.

Answer 2

multiply first equation by 3 and add to 3nd

9x+6y=21

-9x-6y=-21 +

0x+0y=0

0=0

since we got a true statement regardless of the values of x and y, there are infinitely many solutions

also, if you divide the 2nd equation by -3, you will see that the equations are the same