Simultaneous equations - Higher
Sometimes you will be asked to find 2 unknown values by solving 2 equations at the same time. These types of equations are called simultaneous equations.
Simultaneous equations are two equations with two unknowns. They are called simultaneous because they must both be solved at the same time.
The first step is to try to eliminate one of the unknowns.
Solve these simultaneous equations and find the values of x and y.
Add the two equations to eliminate the ys:
So the answers are x = 3 and y = 1
Sometimes you will need to multiply one of the equations before you can add or subtract. Have a look at the activity below.
On other occasions you will need to multiply both equations to find the unknown values. Always look for a way to cancel out one of the unknown terms. Have a go at the question below.
So the answers are a = 3 and b = -1.
We can also use a method of substitution. Look at the following example:
Solve the simultaneous equations:
Equation 1: y - 2x = 1
Equation 2: 2y - 3x = 5
Rearranging Equation 1, we get y = 1 + 2x
We can replace the 'y' in equation 2 by substituting it with 1 + 2x
Equation 2 becomes: 2(1 + 2x) - 3x = 5
2 + 4x - 3x = 5
2 + x = 5
x = 3
Substituting x = 3 into Equation 1 gives us y - 6 = 1, so y = 7.
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