Question

What is the value of the system determinant for the following system of equations?

6x + y = 4
5x + y - 7 = 0

Answer 1

Step 1: Rearrange the two equations in a way where the x&y coefficients are one side while the other numbers (without variables of course) are on the other side.

Step 2: It should be something like this:
6x+y = 4
5x+y = 7

Let's say that [ 6 1 ]
[ 5 1 ] is equal to |A|

Step 3: Set up the determinant equal to the x or y value.
[ 6 1 ] _ [ 4 ]
[ 5 1 ] - [ 7 ]

Step 4: Solve for |A|
det(|A|)
=det([ 6 1 ]
[ 5 1 ])
= 1
Step 5
Replace the first column of the 2 x 2 matrix with [4]
[7]
In this case, the determinant would be [ 4 1 ]
[ 7 1 ]

This determinant would be |Ax| = -3.

Step 6:
Replace the second column of the 2x2 matrix with [ 6 4 ]
[ 5 7 ]
In this case, the determinant would be (6*7) - (4*5) = 35 - 20 = 15

This determinant would be |Ay| = +15

Step 7: Solving for x and y.
x and y could be solved through the following formulas:

x = |Ax|/|A| = -3

y = |Ay|/|A| = +15

I hope this helps =D

Answer 2

You can always plug back the equation to see if the answer is correct or not.
I actually did it myself and it ended up working for me.