Linear Simultaneous Equations Flashcards

All 6 cards in this deck

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

e.g. $2x + y = 7$ and $3x - y = 8$

1. Match the coefficients of one variable: $y$ and $-y$ already match.
2. Add (or subtract) the equations to eliminate it: $5x = 15$, so $x = 3$.
3. Substitute back into one original equation: $y = 1$.

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

e.g. terms $+4y$ and $-4y$

Add when the matching terms have opposite signs; subtract when they have the same sign.
Here $+4y$ and $-4y$: add.

What are the steps to solve linear simultaneous equations by substitution?

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

1. Substitute the expression into the other equation: $3x + (2x + 1) = 11$.
2. Solve for that variable: $5x = 10$, so $x = 2$.
3. Substitute back to find the other: $y = 5$.

What must you do first when a simultaneous equations question is given in words?

Define a letter for each unknown and form two equations from the information.
e.g. 3 teas and 2 coffees cost £7.80 gives $3t + 2c = 7.80$.

True or false? If two linear equations give parallel lines with different intercepts, the simultaneous equations have no solution.

True. Parallel lines never intersect, so there is no pair of values satisfying both.

What do the coordinates of the point where two straight-line graphs cross tell you?

e.g. the graphs of $y = -2x$ and $5x - 9y = -46$ cross at $(-2, 4)$

The solution of the two equations solved simultaneously: $x = -2$, $y = 4$.