Linear Simultaneous Equations Flashcards

All 6 cards in this deck

What are the steps to solve a pair of linear simultaneous equations by elimination?

e.g. $3x+2y=12$ and $x+2y=8$

1. Match coefficients, then add or subtract to eliminate one unknown: subtracting gives $2x=4$, so $x=2$
2. Substitute back into either equation: $2+2y=8$, so $y=3$
3. State both values: $x=2$, $y=3$

When eliminating, do you add or subtract the two equations?

e.g. $3x+2y=12$ and $3x-2y=6$

Same signs on the matched terms: subtract. Different signs: add.
Here the $y$ terms have different signs, so add.

What are the steps to solve simultaneous equations giving $x$ and $y$ in terms of a constant $k$?

e.g. $y=2kx$ and $3x+4y=k$

1. Substitute one equation into the other to eliminate a variable: $3x+8kx=k$
2. Factorise and divide to get the first unknown: $x=\dfrac{k}{3+8k}$
3. Substitute back for the other: $y=\dfrac{2k^2}{3+8k}$

Graphically, what does the solution of two linear simultaneous equations represent?

The coordinates of the point where the two straight lines intersect.

What are the steps to find unknown constants in a curve's equation from points it passes through?

e.g. $y=ax^2+bx$ passes through $(2,20)$ and $(6,12)$

1. Substitute the first point: $4a+2b=20$
2. Substitute the second point: $36a+6b=12$
3. Solve the pair simultaneously: $a=-2$, $b=14$

True or false? A pair of linear simultaneous equations always has exactly one solution.

False. If the lines are parallel there is no solution; if they are the same line there are infinitely many.