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Core Connections Algebra 2, 2013

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Core Connections Algebra 2, 2013 View details

1. Section 6.1

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Exercise 9 Page 259

Does either of the equations have only one variable in it?

(-2,5)

Practice makes perfect

We are given a system of equations and asked to find the pair of (x,y) that satisfies both of the equations. 3 x+8=2 & (I) 7 x+3 y=1 & (II)Notice that in Equation (I) we have only x-terms, so we can start by finding the value of x using this equation.

3x+8=2 7x+3y=1

(I):LHS-8=RHS-8

3x=-6 7x+3y=1

(I):.LHS /3.=.RHS /3.

x=-2 7x+3y=1

Great! Now, to find the value of y, we need to substitute x=-2 into the second equation.

x=-2 7x+3y=1

(II):x= -2

x=-2 7( -2)+3y=1

(II): a(- b)=- a * b

x=-2 -14+3y=1

(II):LHS+14=RHS+14

x=-2 3y=15

(II):.LHS /3.=.RHS /3.

x=-2 y=5

The solution, or point of intersection, to this system of equations is the point (-2,5).

Subchapter links

6.1.1 Creating a Three-Dimensional Model p.259-260

6.1.2 Graphing Equations in Three Dimensions p.263-265

6.1.3 Systems of Three-Variable Equations p.267-268

6.1.4 Solving Systems of Three Equations with Three Unknowns p.271-273

6.1.5 Using Systems of Three Equations for Curve Fitting p.278-281