Algebra Chapter 7
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Lesson quizzes are also available on this website after each section.
Tentative lesson plans are included below as well as notes for each section.
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- Section 7-1
Be precise and use graph paper to see the exact point of intersection between the two equations. Remember to put equation into the form y = mx+b format. The point of intersection will be the ordered pair (x,y) that satifies both equations for the values of x and y.
Recall equations with the same slope and different y intercepts are parallel lines and therefore will have no points of intersection. These systems of equations have no solutions.
Equations with the same slope and the same y intercepts are the same line and therefore will have all points in common. These systems of equations have infinitely many solutions.
Recall if two values are equal, you can substitute in values. 3x + y = 10 and y = x + 2
In these equations we can substitute
y for x+2 into the first equation:
3x + (x + 2) = 10
then solve for x: 4x + 2 = 10
4x = 8
x = 2
Then substitute again y = (2) + 2
y = 4
The solution is x = 2 and y = 4 (2,4)
Recall if a=b and c=d, then a + c = b + d
and a - c = b - d
We can apply this to systems of equations to add or subtract equations with the sme coeffiecient for the x or y variables.
Example: 3x + 4y = 12 and 2x - 4y = 3 Add
3x + 4y = 12
2x - 4y = 3
5x = 15
x = 3
Substitute back in to find y 3(3) + 4y = 12
9 + 4y = 12
4y = 3
y = 3/4 or 0.75
The solution is x =3 and y = 0,75 (3, 0.75)
- Chapter 7 Lesson Plans
Solving systems of Equations through graphing, substitution and elimination. Solving Inequalities with graphing.