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MAT-100C Study Guide - Final Guide: Texas Instruments

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School
Algonquin College
Department
Mathematics
Course
MAT-100C
Professor
Richards

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Document Summary

Problem 1 graphing systems of linear equations. How many solutions does each system have? y 2x 3 y x 1 y 3x 3 y 3x 1. 4x 2y 6 y 2x 3. The three graphs you sketched above show all the possible ways two lines can relate to each other. Fill in the answers for the right column. It shows the graph of a linear equation. Use the line tool to draw a second line on the graph so that the two lines form a linear system with exactly one solution. Use the coordinates and equations tool to find the equations of the two lines. Draw a new line to make a system with no solution. Record the equation of the line in the table. Draw a new line to make a system with infinitely many solutions. Repeat this experiment with the lines you find in the cabrijr files howmany2, howmany3, and howmany4.

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Related Questions


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**the text is what is contained in the picture**

1. Consider first a linear equation: 3x – 1 = 5.

a. Use a graphing utility to show y1= 2x – 1 and y2=5 and determine the point of intersection. Make a sketch and label it.

b. How does the graph in part (a) relate to the solution set of the equation 3x – 1 = 5?

c. To solve the equation 3x – 1 =5 algebraically, the first step is to add 1 to both sides of the equation. Use a graphing utility to show y1=3x and y2=6, and determine the point of intersection. Make a sketch and label it. How does this graph relate to the equation 3x=6?

d. The final step to solve the equation is to divide both sides of the equation by 3. Use a graphing utility to show y1=x and y2=2, and determine the point of intersection. Make a sketch and label it. How does this graph relate to the equation x=2?

e. The algebraic steps to solve the equation 3x – 1 = 5 produce two equations: 3x=6 and x=2. How do the graphs you sketched above represent the fact that these equations are equivalent to the original?