Question

Solve the following system by using graph paper or graphing technology.

3x – 2y = 7
9x – 6y = 3

What is the solution to the system?

A.No Solutions

B.Infinite Solutions

C.(3, 2)

D.(3, –2)

Answer 1

3x - 2y = 7
9x - 6y = 3

You can use either substitution or elimination to solve for the variables. I live elimination better so I will use that to solve this system. And we will eliminate y first to solve for x. Then we can plug x back in to solve for y.

To eliminate y, we first make the y values of both equations the same. This can be done by multiplying the 2 equations.

9x - 6y = 21 --> Here I multiplied both the entire equation 3x - 2y = 7 by 3 so that the y value becomes -6y and then we will be able to eliminate it by adding or subtracting the other equation.
9x - 6y = 3

But after the multiplying by 3, we notice that both equation look the exact same but one equals 21 and the other equals 3? That is not possible because 2 exact same equations should have the same value, but here they don't. This we can confirm because if I were to eliminate y by subtracting the 2 equations, I get this:

9x - 6y = 21
- 9x - 6y = 3
---------------
0 = 18 --> When we subtract the two equations, we are left with an invalid answer.

This means that the system of equations has no solutions.

Therefore, the answer is A. No Solutions.

Answer 2

thanks !