Chapter 11: Q. 311 (page 1159)

In the following exercises, solve the system of equations by using graphing.
$3 x^{2} - y = 0 y = 2 x - 1$

Short Answer

Expert verified

System of equations have no solution.

Step by step solution

Given information

Given two equations are

$3 x^{2} - y = 0 y = 2 x - 1$

Graph first equation

Given equation is

$3 x^{2} - y = 0 3 x^{2} = y y = 3 x^{2}$

we find out the vertex using formula

$x = \frac{- b}{2 a} a = 3, b = 0 x = \frac{- 0}{2 (3)} = 0 y = 3 x^{2} y = 3 {(0)}^{2} = 0 v e r t e x i s (0, 0)$

The value of a=3, a is positive. so the graph of parabola goes up .

x and y intercept is (0,0)

Now graph the parabola

Graph the second equation

$y = 2 x - 1$

substitute x =0 and find out y intercept

substitute y=0 and find out x intercept

$y = 2 x - 1 x = 0 y = 2 (0) - 1 y = - 1 y i n t e r c e p t i s (0, - 1) y = 0 0 = 2 x - 1 1 = 2 x x = \frac{1}{2} x i n t e r c e p t i s (0.5, 0)$

Graph the intercepts and connect it by a line .

Graph both the equations in same plane

Intersection

Both the graphs does not intersects.

So , no solution for these system of equations

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, solve the system of equations by using graphing.
$3 x^{2} - y = 0 y = 2 x - 1$

Short Answer

Step by step solution

Given information

Graph first equation

Graph the second equation

Intersection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Geometry

Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using graphing.3x2-y=0y=2x-1

Short Answer

Step by step solution

Given information

Graph first equation

Graph the second equation

Intersection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Geometry

Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using graphing.
$3 x^{2} - y = 0 y = 2 x - 1$