Simultaneous Equations
Grade 8
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Learning Outcomes
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs
Solve systems of two linear equations in two variables algebraically
Simultaneous Equations
Simultaneous equations are two or more algebraic equations that can be solved at the same time. Linear simultaneous equations with two unknown variables can be solved by using the following methods:
Graphical Method
Elimination Method
Substitution Method
In this lesson, we will focus on solving linear simultaneous equations algebraically using the elimination method, but first, let's have a look
at some graphs.
Graphs of Simultaneous Equations
1
2
3
4
-4
-3
-2
-1
1
2
3
4
The solutions of simultaneous equations with two unknown variables correspond to the point of intersection of their graphs.
-4
-3
-2
-1
Here is a system of two equations:
x + y = 2
y = x + 1
The solution to the simultaneous equations is x = 0.5, y = 1.5
x + y = 2
y = x + 1
Elimination Method
In the elimination method, one variable is eliminated by adding or subtracting the equations. This leaves one equation with one variable.
x + 4y = 6
x + 3y = 4
-
y = 2
Subtracting these equations eliminates the x variable
x + 2y = 6
3x - 2y = 10
+
4x = 16
Adding these equations eliminates the y variable
Example
1
5x + 2y = 24
3x + 2y = 16
-
2x = 8
x = 4
1
2
Substitute into equation
5(4) + 2y = 24
20 + 2y = 24
2y = 4
y = 2
Solve the equation for y
Look for the same coefficient. Subtract if they both have the same sign
1
x = 4, y = 2
The y variable has been eliminated, solve for x
Example
2
2x - 2y = - 6
x + 2y = 3
+
3x = - 3
x = - 1
1
2
Substitute into equation
2(-1) - 2y = - 6
-2 - 2y = - 6
- 2y = - 4
y = 2
Solve the equation for y
Look for the same coefficient. Add if they have different signs
1
x = -1, y = 2
The y variable has been eliminated, solve for x
Practice Questions
1
2
3
4
3x + 2y = 12
x + 2y = 8
3x - y = 10
2x + y = 5
x - 3y = - 17
2x + 3y = 11
3x + 2y = 11
3x + y = 7
Practice Questions - Answers
1
2
3
4
3x + 2y = 11
3x + y = 7
3x + 2y = 12
x + 2y = 8
3x - y = 10
2x + y = 5
x - 3y = - 17
2x + 3y = 11
x = 1, y = 4
x = 2, y = 3
x = 3, y = -1
x = -2, y = 5
THANK YOU
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