Question 175330
Determinants can be used to solve a linear system of equations using Cramer’s Rule.

Cramer’s Rule is used for Two Equations in Two Variables, which is what you have: variables x and y.

2x+3y = 41
2x-3y = -13

To find the determinant, we use:

D = 2(-3) - 2(3)

D = -6 -6

D = -12

To find x use:

x = Dx/D

We already know D, right?

We need to find Dx.

We find Dx = 41(-3) - 3(-13)

Dx =  -123 + 39

Dx = -84

We can now find x.

So, x = -84/-12

Then x = 7

Lastly, we need to find y.

y = Dy/D

We know D to be -12, right?

To find y, we need to first find Dy.

We can find Dy = 2(-13) - 2(41)

Dy = -26 - 82

Dy = -108

We can now find y.

y = -108/-12

y = 9

The solution to the above system of equations in two variables is the point

(7, 9)

The two equations given to you meet or cross each other at the point (7, 9) and so, this is why that particular point is the solution.

Understood?

The answer is choice (A).