Question

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

Answer 1

Answer:

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

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:

$-47c=-248\\47c=248\\c=\frac{248}{47} \\c=5.27$

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)