Non Linear Simultaneous Equations

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.

7x + y2 = - 5, x + y = 1.

Answer:

The final answer is x = - 2, - 3 and y = 3, 4

by: mathqa

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