Simultaneous Equations Flashcards

All 7 cards in this deck

What are the steps to solve simultaneous equations by elimination when a coefficient already matches?

e.g. $2x + y = 7$ and $x + y = 4$

1. Same sign, so subtract the equations to eliminate $y$: $x = 3$
2. Substitute into one equation: $3 + y = 4$
3. Solution: $x = 3$, $y = 1$

What are the steps to solve simultaneous equations when one equation must be scaled first?

e.g. $x + 2y = 8$ and $3x + y = 9$

1. Multiply the first equation by $3$: $3x + 6y = 24$
2. Subtract to eliminate $x$: $5y = 15$, so $y = 3$
3. Substitute back: $x = 2$. Solution $x = 2$, $y = 3$

When neither the $x$ nor the $y$ coefficients match, what do you multiply the two equations by before eliminating?

e.g. $2x + 3y = 13$ and $3x + 2y = 12$

Multiply each equation by a number so that one pair of coefficients becomes equal (their LCM).
e.g. $\times 3$ and $\times 2$ to give $6x$ in both.

What are the steps to solve simultaneous equations by substitution?

e.g. $y = 2x + 1$ and $3x + y = 11$

1. Substitute $y = 2x + 1$ into the other equation: $3x + 2x + 1 = 11$
2. Solve for $x$: $5x = 10$, so $x = 2$
3. Substitute back: $y = 5$. Solution $x = 2$, $y = 5$

True or false? The solutions of a pair of simultaneous linear equations are always positive whole numbers.

False. They can be negative or fractional/decimal, e.g. $x = 6.5$, $y = -2.75$.

When two straight line graphs are drawn on the same axes, what does the point where they cross tell you?

e.g. the lines cross at $(3, -1)$

The solution of the simultaneous equations: the $x$-coordinate is $x$ and the $y$-coordinate is $y$.

e.g. $x = 3$, $y = -1$

True or false? A solution read off the point where two graphs cross may only be approximate.

True. The specification asks for approximate solutions from a graph; exact values come from solving algebraically.