Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
1. Solving Systems of Linear Equations by Graphing
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Exercise 21 Page 221

Rewrite the system in slope-intercept form and check whether the equations match the graphed lines.

Error: The graph of the second equation is incorrect.
Correction: See solution.

Practice makes perfect

Let's check whether the equations were graphed correctly by rewriting both of them in slope-intercept form first.

x-3y=6 & (I) 2x-3y=3 & (II)
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Write in slope-intercept form

(I), (II): LHS+3y=RHS+3y

x=6+3y 2x=3+3y
x-6=3y 2x=3+3y
x-6=3y 2x-3=3y

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

13x-2=y 23x-1=y

(I), (II): Rearrange equation

y= 13x-2 y= 23x-1
Now let's analyze the two graphs by finding their y-intercepts and slope. Then, we can check whether the graphed lines match our equations in slope-intercept form.

We can write the equations of the lines in slope-intercept form. y= 13x-2 y= 23x-3 Notice that the second equation does not match our second equation. This means that 2x-3y=3 was not graphed correctly. y= 13x-2 y= 23x-1 Let's correct this error by graphing the system of equations that we found previously and determining the point of intersection of the lines.

The solution of the system is (-3,-3).