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Chapter 11: Q. 62 (page 773)

In Problems 57-64, use a graphing utility to solve each system of equations. Express the solution(s) rounded to two decimal places.

role="math" localid="1646903798288" x4+y4=6xy=1

Short Answer

Expert verified

The graph for the system of equations x4+y4=6xy=1is,

From the graph, the solutions of the given system are,role="math" localid="1646904365592" 0.64,1.56,1.56,0.64,-0.64,-1.56,-1.56,-0.64.

Step by step solution

01

Step 1. Given information

x4+y4=6xy=1

First solve the given equations for y.

Let us consider the first equation.

x4+y4=6y4=6-x4lny4=ln6-x44lny=ln6-x4lny=ln6-x44y=eln6-x44

Next consider the second equation.

xy=1y=1x

02

Step 2 Now sketch a graph for the obtained equations.

In the graph, the two equations are intersecting at four points. They are, 0.64,1.56,1.56,0.64,-0.64,-1.56,-1.56,-0.64. So, the system has four solutions.

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Most popular questions from this chapter

In Problems, use the division algorithm to rewrite each improper fraction as the sum of a quotient and proper fraction. Find the partial fraction decomposition of the proper fraction. Finally, express the improper fraction as the sum of a quotient and the partial fraction decomposition.

x5+x4-x2+2x4-2x2+1

Verify that the values of the variables listed are solutions of the system of equations.

3x+2y=2x-7y=-30x=-2,y=4;(-2,4)

If the solution to a system of two linear equations containing two unknowns is x=3,y=-2, then the lines intersect at the point _________.

Graph the equation:y2=x2-1

Solve each system of equations. If the system has no solution, say that it is inconsistent.
3x-6y=25x+4y=1
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