Solve 2x + 4y = 6, x + 2y = 5 by Cramer's rule

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The question

Question: solve 2x + 4y = 6 and x + 2y = 5 by Cramer's rule.

We call them ① and ②.

We want the x and y that make both true.

Cramer's rule uses three determinants: D, D x and D y.

Then x is D x over D, and y is D y over D.

1 Find D

D: the numbers in front of x and y, in the same places as in the equations.

So D = 2 × 2 − 1 × 4.

2 times 2 is 4.

1 times 4 is 4.

4 minus 4 is 0.

So D = 0.

D is 0.

Dividing by 0 is impossible, so Cramer's rule gives no single answer.

The two lines are parallel, or the same line.