Quadratic Simultaneous Equations Flashcards

All 5 cards in this deck

What are the steps to solve a linear and a second-order pair of simultaneous equations?

e.g. $y=x+1$ and $x^2+y^2=25$

1. Rearrange the linear equation for one unknown: $y=x+1$
2. Substitute into the second-order equation and simplify: $x^2+x-12=0$
3. Solve, then substitute each value back: $(3,4)$ and $(-4,-3)$

How many solutions can a pair of one linear and one second-order equation have, and what do they represent?

Up to two pairs of values, each pair being the coordinates of a point of intersection of the line and the curve.

True or false? To solve a linear and a second-order equation, you substitute the second-order equation into the linear one.

False. Rearrange the linear equation and substitute that expression into the second-order equation.

After substituting, the resulting quadratic has no real solutions. What does this tell you about the line and the curve?

They do not intersect — there are no solutions to the simultaneous equations.

True or false? If you find $x=3$ or $x=-4$ and $y=4$ or $y=-3$, any pairing of the values is a solution.

False. Each $x$ must be paired with the $y$ found by substituting that same $x$.