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This is one of our many quizzes on Graphing systems of nonlinear equations. Click on this to access more such competitive quizzes on 2D Coordinate Geometry.

Graphing systems of nonlinear equations Quiz 2

mathematics

 Is the system $y = 5x,\,{y^2} = 7{x^2} - 1$ a nonlinear system?

 A nonlinear system must have at least one equation that is not linear, that is, it should not be of the form $ax + by + c = 0$

As the degree of the second equation is more than 1, so the given system is nonlinear.

 Determine the solution of the nonlinear function shown on the graph $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/a6ed66d3-d8be-45c1-a7e8-92d3fcec00551082126632959311979.png"/>

 The points of intersection of the functions in a system are the solutions of the system.

We can see from the graph that the two functions intersect at the points $(0,0)$ and $( - 1, - 4)$ .

 Find the solution of the nonlinear system: $ \\ y = 2{x^2} - 5 \\ y = 4x + 25$

 To find the solution of a nonlinear system, we substitute the value of one variable from one of the equations into the other.

We are given $y = 2{x^2} - 5$ and $y = 4x + 25$ , so $  2{x^2} - 5 = 4x + 25 \\   \Rightarrow 2{x^2} - 4x - 30 = 0 \\   \Rightarrow {x^2} - 2x - 15 = 0 \\   \Rightarrow {x^2} - 5x + 3x - 15 = 0 \\   \Rightarrow (x + 3)(x - 5) = 0 \\   \Rightarrow x =  - 3,\,x = 5 \\  $ At $x =  - 3$ , we get $y = 13$ $ \\ $ At $x = 5$ , we get $y = 45$

 The nonlinear system: $y =  - 3x + 11$ , $y = 7{x^2} + 1$ is represented correctly by which of the following graphs?

 The graph of a system of nonlinear equations can be made by first drawing graph of each equation individually and then combining them.

Graph of $y =  - 3x + 11$ is  $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/f4c19201-4789-4ff6-9a1b-a05d5efb3450873665761189728561.png"/> $ \\ $ Graph of $y = 7{x^2} + 1$ is $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/48b47c46-5538-459a-ad69-a8c246476c995919384227875755968.png"/> $ \\ $ Graph of the combination of $y =  - 3x + 11$ and $y = 7{x^2} + 1$ is $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/77519f78-2f3c-44da-a74f-d9a3377503351717582632264726709.png"/>

 From the graph of the system: $ \\ y = {x^2} + 2x - 14 \\ y = x - 8 \\ $ What are its solutions from the graph that are mathematically verified?

 The solutions can be obtained mathematically by substituting the value of one of the variables and graphically by finding the point of intersection of the given functions.

The graph of the nonlinear system $y = {x^2} + 2x - 14$ and $y = x - 8$ is $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/73ea9479-c9c2-4782-a2cd-48eca5f53009302516874357142325.png"/> $ \\ $ From the graph, we see that the solutions of the system are $( - 3, - 11)$ and $(2, - 6)$ $ \\ $ Verifying solution mathematically – $ \\ {x^2} + 2x - 14 = x - 8 \\   \Rightarrow {x^2} + x - 6 = 0 \\   \Rightarrow {x^2} + 3x - 2x - 6 = 0 \\ \Rightarrow (x + 3)(x - 2) = 0 \\   \Rightarrow x =  - 3,\,x = 2 \\  $ At $x =  - 3,\,y =  - 11$ $ \\ $ At $x = 2,\,y =  - 6$