subject: Non Linear Simultaneous Equations [print this page] A non-linear simultaneous equation is an equation in more than one variable and has a power of two or higher. In this lesson, we shall see how to solve these types of equation. There are three methods to solve these equations they are -substitution method, elimination methods and graphing method.
We will discuss the substitution method in this lesson
Example Problems for Non Linear Simultaneous Equations
Ex 1:
Solve the non linear simultaneous equations and find the value of x and y.
x2 - 4y = 12.
5x + y = 8
Sol:
Given equations
x2 - 4y = 12 equation (1)
5x + y = 8 equation (2)
From equation 2
y = 8 - 5x
Substitute y value in equation 1, we get
x2 - 4(8 - 5x) = 12
After expanding the above equation, we get
x2 - 32 + 20x = 12
Solve the above equation by using factorization, we get
(x - 2) (x + 22) = 0
Therefore,
x = 2 and x = - 22
Substitute the x values in equation 1, we get
For x = 2,
The value of y = - 2
For x = - 22
The value of y = 118
Answer:
The final answer is x = 2 , - 22 and y = - 2, 118
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Ex 2:
Find the non linear simultaneous equations and find the value of x and y.
y = 4x - 3
x2 - y = 0
Sol:
y = 4x - 3 equation (1)
x2 - y = 0 equation (2)
Substitute the equation 1 in equation 2
x2 - (4x - 3) = 0
x2 - 4x + 3 = 0
After solving , we get
(x - 1) (x - 3) = 0
x = 1 and x = 3
Substitute the x value in equation 1, we get
For x = 1,
The value of y = 1
For x = 3,
The value of y = 9
Answer:
The final answer is x = 1, 3 and y = 1, 9.
Practice Problems for Non Linear Simultaneous Equations
1) Solve the non linear simultaneous equations and find its solution.
x2 - y = 12, - 3x + y = 6.
Answer:
The final answer is x = 3, 6 and y = - 3, 24
2) Solve the non linear simultaneous equations and find its solution.
