Solve the simultaneous equations. You must show all your working.
$2x + y = 3$
$x – 5y = 40$
▶️ Answer/Explanation
Ans: x = 5, y = -7
From first equation: y = 3 – 2x
Substitute into second equation: x – 5(3 – 2x) = 40
Simplify: x – 15 + 10x = 40 → 11x = 55 → x = 5
Substitute x back: y = 3 – 2(5) = -7
Natalie buys 4 tomato plants and 3 pepper plants for $9.35 .
Samir buys 2 tomato plants and 11 pepper plants for $16.55 .
Write down a pair of simultaneous equations and solve them to find the cost of one tomato plant and the cost of one pepper plant.
You must show all your working.
▶️ Answer/Explanation
Ans: Tomato plant $1.41, Pepper plant $1.25
Let t = tomato plant price, p = pepper plant price.
Equation 1: 4t + 3p = 9.35
Equation 2: 2t + 11p = 16.55
Multiply Equation 2 by 2: 4t + 22p = 33.10
Subtract Equation 1: 19p = 23.75 → p = 1.25
Substitute p into Equation 1: 4t + 3.75 = 9.35 → t = 1.40