Give feedback
Chapter overview
Learning goals
Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
Other graphs
Ratio
Proportion
Rates of change
Shapes
Properties of shapes
Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
Simultaneous equations involves solving two (or more) equations, where the answers work in all equations given. The idea is that there is a set of solutions that work in both the equations. For two unknowns, there needs to be two equations to solve. Simultaneous equations can be solved using the elimination method.
A) Check if the equations need to be rearranged or multiplied up for them to be written in the correct format. Write out the equations, and number them.
B) Decide whether to add or subtract equations, and solve for one of the variables. Use the rule:
Same sign | Subtract |
Different sign | Add |
C) Substitute the answer obtained into one of the equations, and solve for the other variable.
D) Check both answers in the other equation.
$\begin {aligned}7c+5t &=29 &\textcircled{1} \\7c+8t&= 38 &\textcircled{2} \\\underline{\qquad \quad}& \underline{\qquad \qquad \quad} \\3t&=9 &\textcircled{2} - \textcircled{1}\\t&=3 \\\\7c +5\times3 &=29 \\7c &=14 \\c&=2 \\\\7\times2 + 8\times 3 &=38 \\\underline {c=2, t=3}\end {aligned}$
$\begin {aligned}7c+2d &=2 &\textcircled{1} \\-7c-5d&= 16 &\textcircled{2} \\\underline{\qquad \quad}& \underline{\qquad \qquad \quad} \\-3d&=18 &\textcircled{2} + \textcircled{1}\\d&=-6 \\\\7c +2\times-6 &=2 \\7c &=14 \\c&=2 \\\\-7\times2 -5\times -6 &=16 \\\underline {c=2, d=-6}\end {aligned}$
$\begin {aligned}5p+6q&=17 \\2p+3q&=5 \qquad &\times2\\\\5p+6q&=17 \qquad &\textcircled{1} \\4p+6q&=10 \qquad &\textcircled{2} \\\underline{\qquad \quad}& \underline{\qquad \qquad \quad} \\p&=7 \qquad &\textcircled{1} - \textcircled{2}\\\\5\times7 +6q &=17 \\6q &=-18 \\q&=-3 \\\\2\times7 +3\times -3 &=5 \\\underline {p=7,q=-3}\end {aligned}$
Simultaneous equations involves solving two (or more) equations, where the answers work in all equations given. The idea is that there is a set of solutions that work in both the equations. For two unknowns, there needs to be two equations to solve. Simultaneous equations can be solved using the elimination method.
A) Check if the equations need to be rearranged or multiplied up for them to be written in the correct format. Write out the equations, and number them.
B) Decide whether to add or subtract equations, and solve for one of the variables. Use the rule:
Same sign | Subtract |
Different sign | Add |
C) Substitute the answer obtained into one of the equations, and solve for the other variable.
D) Check both answers in the other equation.
$\begin {aligned}7c+5t &=29 &\textcircled{1} \\7c+8t&= 38 &\textcircled{2} \\\underline{\qquad \quad}& \underline{\qquad \qquad \quad} \\3t&=9 &\textcircled{2} - \textcircled{1}\\t&=3 \\\\7c +5\times3 &=29 \\7c &=14 \\c&=2 \\\\7\times2 + 8\times 3 &=38 \\\underline {c=2, t=3}\end {aligned}$
$\begin {aligned}7c+2d &=2 &\textcircled{1} \\-7c-5d&= 16 &\textcircled{2} \\\underline{\qquad \quad}& \underline{\qquad \qquad \quad} \\-3d&=18 &\textcircled{2} + \textcircled{1}\\d&=-6 \\\\7c +2\times-6 &=2 \\7c &=14 \\c&=2 \\\\-7\times2 -5\times -6 &=16 \\\underline {c=2, d=-6}\end {aligned}$
$\begin {aligned}5p+6q&=17 \\2p+3q&=5 \qquad &\times2\\\\5p+6q&=17 \qquad &\textcircled{1} \\4p+6q&=10 \qquad &\textcircled{2} \\\underline{\qquad \quad}& \underline{\qquad \qquad \quad} \\p&=7 \qquad &\textcircled{1} - \textcircled{2}\\\\5\times7 +6q &=17 \\6q &=-18 \\q&=-3 \\\\2\times7 +3\times -3 &=5 \\\underline {p=7,q=-3}\end {aligned}$
Solving equations
FAQs
Question: What is the elimination method?
Answer: The elimination method means adding or subtracting the two equations to eliminate one of the variables. Only one equation should be left, with one unknown variable, so it is possible to solve the equation. This value can be used to help solve for the other variable.
Question: What are the rules of simultaneous equations when using the elimination method?
Answer: If the signs are different, add the equations. If the signs are the same, subtract them.
Question: What are the methods for solving simultaneous equations?
Answer: You can solve simultaneous equations using the elimination method, the substitution method, or graphically.
Theory
Exercises
© 2020 – 2023 evulpo AG
Your data protection
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners who may combine it with other information that you’ve provided them or that they’ve collected from your use of their services. By clicking on either "Accept cookies" or "Necessary cookies only", you agree to this (read more in our Privacy Policy). Privacy Policy