Question

3. Adam bought 3 pens and 4 pencils for $4.25. Lily bought 2 pens and 6 pencils for $4.50. How much is a pen? a pencil?​

Answer 1

Make two equations
Let x = pen
Let y = pencil
3x + 4y = 4.25
2x + 6y = 4.50
Make both coefficients equal
(3x + 4y = 4.25) * 2
(2x + 6y = 4.50) * 3
6x + 8y = 8.5
6x + 18y = 13.5
Subtract both sides
-10y = -5, y = 0.50
3x + 4(0.50) = 4.25
3x + 2 = 4.25
3x = 2.25, x = 0.75

Pen = $0.75
Pencil = $0.50