4x-2y=-30

First create a matrix of coefficients for x and y:

( 2 -4 )

( 4 -2 )

The first column contains the x coefficients and the second column the y coefficients.

Now work out the determinant for the matrix:

| 2 -4 |

| 4 -2 |=(2)(-2)-(-4)(4)=-4+16=12.

To evaluate the determinant, multiply diagonally as shown: subtract the products as shown. The determinant, which we’ll call D, has a value of 12. We’ll need this later.

To find x, replace the x column by the column for the constants:

| -18 -4 |

| -30 -2 |

and evaluate this new determinant=(-18)(-2)-(-4)(-30)=36-120=-84.

Divide by D: -84/12=-7, so x=-7.

Now find y the same way.

The determinant for y is:

| 2 -18 |

| 4 -30 |=(2)(-30)-(-18)(4)=-60+72=12. Divide by D: y=12/12=1.

So the solution using Cramer’s Rule is x=-7, y=1.

Check the solution by putting these values of x and y into the original equations:

2×(-7)-4×1=-14-4=-18 OK

4×(-7)-2×1=-28-2=-30 OK solution confirmed.

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