System Of Equations
By: Eric D.
Solving By Graphing
For this equation you must move the x variable to the opposite side.
Your new equations will be
After getting the y to be by it self, you then need to divide everything by the y variables coefficient. After dividing each side, your new equations will be
You then will graph these equations, like on the picture bellow this.
Solving By Substitution
Now that you have x=10-4y, you have to substitute it into the other equation, 3x-5y=13.
Subtract 30 from each side
Divide each side by -17
Now that you have y, you have to put it into both equations to get x, make sure x is the same number for both.
Add 5 to each side
Divide each side by 3
Now use this x and y for the other equation
The answer for this set of equations is x=6 and y=1. (6,1)
Solving By Elimination
After doing this step you must make one of the variables equal zero, for example, x+-x=0x, or -5x+5x=0x.
For this set of equations I'll multiply the first equation by negative 3.
Now add this to the other equation.
You will get
This means y=7.
Now you put y=7 back into the original equations.
Subtract 5 from each side
For the other equation
The answer for this set of equation is x=16 and y=7. (16,7)
When should I use Substitution? When should I use Elimination? When should I use Graphing?
You should use Elimination whenever you have a question that has the x and y variable on the same side of the equation for both equations.
You should use graphing whenever you have the y variable isolated with and the coefficient is one for both variables.
Types of Solutions
There is No Solution which happens when there is not possible answer. On a graph the would never intersect, they would always be parallel.
There is Infinite Solutions which is when the line always intersect. On a graph they would be a single line.
There is One Solution which is when there is a single answer, it intersects at a single point. On a graph it would be two lines intersecting only for one point of the line.
Solving By Writing The System Of Equations
In this equation, I will use elimination to solve it.
Divde each side by -12
Putting this into the original equations
Subtract 22.50 from each side
Now try this with your other equations.
This means each quart is 2 dollars,and each gallon is 2.25 dollars. (2.25, 2) (g,q)
Solving Word Problems
Like the previous question, I will use elimination.
Divide by 2 on each side
Now use this for the original equations.
Subtract 48 from each side
Now use this for the other equation
This means there is a flat fee of 15 dollars, and a charge of 12 dollars per hour. (15,12)