Question

22a-3c=-6 a+2c=11 WHAT IS THE SOLUTION (a,c) to this system of linear equations?

Answer 1

The solution (a,c) is (0.46, 5.27)

Step-by-step explanation:

Let's write down the system

`22a-3c=-6\\a+2c=11`

To solve this system we are going to use the method of reduction, we are going to multiply the second equation by -22 so that our a's disappear when we sum up the equations.

Multiplying by -22 we get:

`22a-3c=-6\\-22a-44c=-242`

Now if we sum up both equations we have:

`-47c=-248\\47c=248\\c=(248)/(47) \\c=5.27`

Now we substitute c in our second equation:

`a+2c=11\\a+2(5.27)=11\\a+10.54=11\\a=11-10.54\\a=0.46`

Thus, the solution (a,c) is (0.46, 5.27)