Flashcards · 12 cards

Linear & simultaneous equations

Say the answer to yourself, then check. Cards you know come back less and less often; cards you don't come back tomorrow.

Rule
The one rule for solving an equation?
Answer
Do the same to both sides, so it stays balanced.
Do the same to both sidesTaking 2x from both pans keeps the balance level
From the lesson: Solving linear equations
Know it
How do you clear the fractions from an equation?
Answer
Multiply every term by the LCM of the denominators, including the terms with no fraction.
From the lesson: Solving linear equations
Know it
$\dfrac{3m - n}{2m + n} = \dfrac14$ . What is the next step?
Answer
Cross-multiply: $4(3m - n) = 2m + n$ . Don't set top equal to top and bottom equal to bottom.
From the lesson: Solving linear equations
Rule
What is the solution of two simultaneous equations, on a graph?
Answer
The point where the two lines cross: the pair $(x, y)$ that lies on both.
The solution is the crossing pointThe pair (x, y) that lies on both lines
From the lesson: Simultaneous equations
Know it
How does elimination work?
Answer
Make the number in front of one letter the same in both equations, then add or subtract the equations to remove that letter.
From the lesson: Simultaneous equations
Know it
How does substitution work?
Answer
Make one letter the subject of one equation, then put that into the other equation.
From the lesson: Simultaneous equations
Know it
Simultaneous equations in $\frac1x$ and $\frac1y$ : how do you solve them?
Answer
Let $a = \frac1x$ and $b = \frac1y$ , solve for $a$ and $b$ , then turn them back into $x$ and $y$ : the question wants $x$ and $y$ .
From the lesson: Simultaneous equations
Know it
One linear and one quadratic equation: how do you start?
Answer
Make one letter the subject of the linear equation and substitute it into the quadratic.
From the lesson: Simultaneous equations
Know it
A routine for word problems?
Answer
Choose a letter for each unknown and say what it stands for. Write each fact as an equation. Solve, then answer exactly what was asked, with units.
From the lesson: Turning words into equations
Rule
A journey in two parts at different speeds: how do you find the total time?
Answer
Work out the time for each part with $T = \dfrac DS$ and add the times. Don't add or average the speeds.
Speed, distance, timeCover the one you want: T = D ÷ S for each part
From the lesson: Turning words into equations
Which method?
WAEC 2020 · Paper 1 · Q10
Solve $3x - 2y = 10$ and $x + 3y = 7$ simultaneously.
Which method is quickest here?
Answer
Substitution: the second equation gives $x = 7 - 3y$ straight away. Put it into the first.
From the lesson: Simultaneous equations Try the question
Which method?
WAEC 2018 · Paper 2 · Q2 (a)
Musa is three years older than Manya. Seven years ago, Musa was twice as old as Manya. How old are they now?
How do you set up the equation?
Answer
Let Manya be $x$ , so Musa is $x + 3$ . Seven years ago they were $x - 7$ and $x - 4$ , and "twice as old" gives $x - 4 = 2(x - 7)$ .
From the lesson: Turning words into equations Try the question