If one is in ratio, the other is zero

Anurupye Shunyamanyat

If one column of coefficients in a pair of simultaneous equations is in the same ratio as the constants, the other variable is zero. This lets you solve the system almost by inspection.

How It Works

1.Given simultaneous equations: a₁x + b₁y = c₁ and a₂x + b₂y = c₂.
2.Check if the x-coefficients and constants are in the same ratio: a₁/a₂ = c₁/c₂.
3.If they are, then y = 0 (the variable whose column is NOT in ratio).
4.Substitute y = 0 back into either equation to find x.
5.This works because the y-terms must cancel for the ratio to hold.

Examples

3x + 4y = 12, 6x + 7y = 24

Step 1 / 4

System: 3x + 4y = 12 and 6x + 7y = 24

Eq 13x + 4y = 12

Eq 26x + 7y = 24

Try It Yourself

2x + 3y = 6, 4x + 5y = 12 → x = ?

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