Use a graphing utility to solve each system of equations. Express the solution(s) rounded to two

Use a graphing utility to solve each system of equations....

Key Concepts

Numerical Approximation and Rounding

Numerical approximation is the process of finding estimates for solutions when exact answers are hard to obtain. In many practical applications, including the use of graphing utilities, solutions are computed as decimals and are then rounded to a specified degree of accuracy (such as two decimal places) to provide a clear and usable result.

Graphical Method and Intersection Points

The graphical method involves plotting each equation on the same coordinate system and identifying the points where the graphs intersect. These intersection points represent solutions that satisfy all equations in the system. This technique is particularly valuable for visualizing and approximating the solutions of both linear and nonlinear systems.

System of Equations

A system of equations consists of multiple equations that are solved together because they share common variables. The solution to the system must satisfy every equation simultaneously, which can be obtained through various methods including algebraic manipulation, substitution, elimination, or graphical analysis.

Nonlinear Equations

Nonlinear equations are equations that involve variables raised to powers other than one, products of variables, or other non-linear operations. Solving nonlinear systems (where at least one equation is nonlinear) can become challenging because they may yield multiple or no solutions, and graphical methods or numerical approximations are often useful.

Transcript

00:01 And this problem, we're asked to solve the system of equations using our graphing calculator.

00:08 So the first thing we need to do is solve for y for each one of these equations.

00:14 So from the first equation, if we solve for y, you need to subtract x to the fourth on both sides.

00:20 So therefore, it's going to become y to the fourth equals to 12 minus x to the fourth.

00:26 And to get rid of the fourth power, you're going to take fourth root on both sides.

00:31 And just like with the square root, whenever you're taking fourth root on both sides, you're going to have a plus -minus answer.

00:38 So y equals to fourth root of 12 minus x to the fourth.

00:44 And then for the second equation to solve for y, i need to divide both sides by x.

00:49 So therefore, y -square equals to 2 over x.

00:54 And to get rid of the square, you're going to take square root both sides.

00:58 So therefore, y is going to be equals to plus or minus the square root of 2 over x.

01:04 So for this system of equations, there are four equations you have to type in your calculator.

01:10 So go to turn on your calculator, go to y equals, and here are my four equations.

01:18 Y1 is the positive fourth root of 12 minus x to the fourth.

01:23 Y2 is going to be negative.

01:26 So let me get rid of that.

01:27 Let me type that again.

01:30 Negative, negative fourth root.

01:38 Okay, let me try again.

01:40 I'm going to type in fourth root first.

01:44 So fourth root of 12 minus x to the fourth.

01:50 And then i'm going to add a negative in front of it and negative.

02:00 There you go.

02:02 And then my y3 is positive square of 2 over x, and my y4 is going to be negative square of 2 over x.

02:09 So now let's press graph.

02:22 Okay, so as you can see, for this system of equations, there are going to be four solutions because there are four intersections...

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