Solving Simultaneous Equations - Substitution Method
This lesson covers:
- Introduction to non-linear simultaneous equations
- How to solve non-linear simultaneous equations by the substitution method
Solving simultaneous equations by substitution
Sometimes it isn't possible to solve simultaneous equations by elimination. This is usually when one of the equations is quadratic. To solve these simultaneous equations we use a method called substitution. This is done by substituting one equation into the other one. The equations below would need to be solved by the substitution method.
x2 + 2y = 9
y - x = 3
Worked example 1: Solving simultaneous equations by substitution.
In this method, we will solve the following simultaneous equations by substitution.
- x2 + 2y = 9
- y - x = 3
Worked example 2: Solving simultaneous equations by substitution.
In this method, we will solve the following simultaneous equations by substitution.
- x2 + 3y = 21
- y - 3x = -5
Worked example 3: Solving simultaneous equations by substitution.
In this method, we will solve the following simultaneous equations by substitution.
- x2 + 3y = 7
- 2x + y = 5
Solve the following simultaneous equations using the substitution method.
- x2 + 7y = 2
- 4x + y = 11
(12, -2) and (25, -3)
(3, -12) and (25, -2)
(-25, 89) and (-3, 12)
(25, -89) and (3, -1)
|
Solve the following simultaneous equations using the substitution method.
- x2 + 6y = -3
- 4x - y = 14
(122,-2) and (27,-3)
(-27, -122) and (3,-2)
(27, 122) and (-3, 2)
(3,-122) and (-27,-2)
|
Solve the following simultaneous equations using the substitution method.
- y = x2 - 5
- y + 2 = 2x
(122, -2) and (27, -3)
(4, 3) and (12, -2)
(-3, -4) and (-4, -1)
(3, 4) and (-1, -4)
|
Solve the following simultaneous equations using the substitution method.
- 5x + 3y = 14
- y = 2x + 1
(3, 4)
(-1, -3)
(1, 3)
(-3, -4)
|
Solve the following simultaneous equations using the substitution method.
- 4x + 3y = -3
- y = 2x - 16
(-1, -3)
(4.5, -7)
(-3, -7)
(-3, 4.5)
|