Question

Janelle is five years younger than Louisa. In three years, Janelle will be half Louisa’s age. If j represents Janelle’s age now and l represents Louisa’s age now, which matrices represent the situation?

Answer 1

Let j = Janelle’s current age, l = Louisa’s current age.

Equations:
1) j = l − 5 → j − l = −5
2) j + 3 = 1/2 (l + 3) → 2(j + 3) = l + 3 → 2j − l = −3

Matrix form (coefficient matrix · variable vector = constant vector):
[ [1 −1],
[2 −1] ] [ j ] = [ −5 ]
[ l ] [ −3 ]

Augmented matrix form:
[ 1 −1 | −5 ]
[ 2 −1 | −3 ]