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Classwork
Friday, December 14, 2020
Solving Systems of Equations Through Elimination
Obj: How do we solve systems of equations using elimination?
When two equations are both writtien in Standard form, such as Ax + By = C,
it is not as easy to use substitution to solve the system of equations. This
is because there is no equation with either x = or y = to provde a replacement.
Is there another way to combine two equations in Standard Form? Yes! There is!
We could trying adding the two equations together or subtraction one from the other. This is how we solved the popcorn and soda problem from last week!
For this to work, the two equations need to have a coefficient in common. For example
2x + 3y = 34
6x - 3y = 30
8x = 64
x = 8
Now find y:
2(8) + 3y = 34
16 + 3y = 34
3y = 18
y = 6
Friday, December 11, 2020
Solving Systems of Equations Through Substitution
Obj: How do we solve systems of equations using substitution?
We know how to find when two functions are equal to each other by setting the functions equal to each other. We can do something similar when two equations are in a form beginning with y=.
For example, in the system of equations
y = 2x + 3
y = 5x - 18
the y in the first equation can be replaced with 5x - 18 from the second equation. This is because y, 2x + 3, and 5x - 18 are all equivalent expressions.
This means that
5x - 18 = 2x + 3
By solving this one equation with one variable (there is no y), we can solve for x. Once we know what x is, we can find what y is.
This can be seen on a graph as the intersection of two lines.
Thursday, December 10, 2020
Solving Systems of Equations Through Substitution
Obj: How do we solve systems of equations using substitution?
When we substitute with functions, we usually replace a variable in an algebraic expression with a number.
However, you don't have to replace it with a number. Any variable can be replaced with another algebraic expression.
For example, in the system of equations
2x + y = 9
y = 2x - 3
the y in the first equation can be replaced with 2x - 3 from the second equation. This is because y and 2x - 3 are equivalent expressions.
This means that
2x + 2x - 3 = 9
By combining the equations into one, we can solve for x, and then solve for y.
This can be seen on a graph as the intersection of two lines.
Wednesday, December 9, 2020
Systems of Equations
Obj: How do we solve systems of equations?
Table we used rebus puzzles to solve more complex Algebra problems, by breaking down the complicated into simpler objects using pictures
A "system" of equations is just two (or more) equations that use the same variables. The solution is the ordered pair (x, y) that makes both (or all) or the equations true at the same time.
This can be seen on a graph as the intersection of two lines.
Tuesday, December 8, 2020
Parallel Lines
Obj: How do we find the equation of a line parallel to a given line that goes through a given point?
We know from last week how to graph a line parallel to a given line on a graph but how can we do it with just an equation?
Parallel lines have the SAME SLOPE. So a line with an equation like:
y = 2x + 1
would be parallel to lines with equations like:
y = 2x + 2
y = 2x + 5
y = 2x - 7
y = 2x
y = 2x + 37.41
etc.
Monday, December 7, 2020
Test Day
I hope you studied. Do your best.
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