Solving linear systems with graphing 7.1 answers

Saxon Math, Course 2

1st EditionHake, Stephen

4,848 solutions

Precalculus

2nd EditionCarter, Cuevas, Day, Malloy

8,897 solutions

Algebra and Trigonometry: Structure and Method, Book 2

1st EditionBrown, Dolciani, Kane, Sorgenfrey

8,444 solutions

Algebra 2 Common Core

1st EditionBasia Hall, Charles, Kennedy

7,538 solutions

Introduction:
What you are doing in this unit is finding the intersect of 2 equations. First you have to find the 2 lines and then find the point where they intersect. This will never happen with parallel lines. In the solution of a linear system,each equation should be satisfied. The solution needs to lie on the graph of both equations. If the solution has an inter value than you can find the solution using graphical methods.
(Note: the more accurate your line is, the better your answer will be).

Lesson Video

Vocab:Linear System: A linear system is a mathematical model of a system based on the use of a linear operator.

Solution: When dealing with linear systems, the solution to a problem is most commonly a point (x,y) that is able to solve both equations.

Example Problems:

1) Graph the system of equations. Determine whether the system has one solution, no solution, or infinitely any solutions. If the system has a solution, name it.

y = x

y = 8 – x

The solution is the intersection shown below.

The answer is (4,4) it solves both.

2) The people of the island nation of Iceland were converted to Christianity from the old Norse polytheistic religion starting around 1000 A.D. Suppose

represents the percent of Icelanders professing Christianity at time t, and

represents the percent that was non–Christian. Find the time at which there were equal numbers of Christians and non–Christians in Iceland. (Hint: let t = 0 represent the year 1000.)

From the graph below it is possible to tell that these populations will never be the same.

No solution.

http://hotmath.com/help/gt/genericalg1/section_5_1.html

Using your calculator:

Video Lesson

YouTube Video

Graph and Check Method

To use the graph-and-check method to solve a system of linear equations in two variables,use the following steps:
1) Write each equation in a form that is easy to graph.
2) Graph both equations in the same coordinate plane.
3) Estimate the coordinates of the point of intersection.
4) Check the coordinates algebraically by substituting into each equation of the original linear system.

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Systems of Linear equations: Graphing