Forming & Solving Equations Flashcards

All 3 cards in this deck

What are the steps to form and solve an equation from a worded context?

e.g. a rectangle of width $x$ and length $x+3$ has area $40$

1. Write an expression for the quantity described: area $= x(x+3)$
2. Set it equal to the given value and rearrange to $=0$: $x^2+3x-40=0$
3. Solve and interpret: $(x+8)(x-5)=0$, so $x=5$ (reject $x=-8$)

When a quadratic from a length, area or volume problem gives a negative solution, what do you do?

Reject it — a length cannot be negative — and state only the valid solution.

What are the steps to find where a line meets a circle centred on the origin?

e.g. $x^2+y^2=25$ and $x = 2y-5$

1. Substitute the line into the circle equation: $(2y-5)^2+y^2=25$
2. Expand and solve the quadratic: $5y^2-20y=0$, so $y=0$ or $y=4$
3. Find the matching $x$ values and give coordinates: $(-5,0)$ and $(3,4)$