System of Equations
By Tessa Cisco
What Is A System Of Equations?
A system of equations is a set of two or more equations that have the same unknown. The answer to a system of equations is the intersection point.
Three Types of Systems of Equations
There are three types of systems of equations, one solution, no solution, and infinitely many.
One Solution
If the two lines are graphed and they intersect at one point, then the answer is one solution. The solution is the intersection point.
No Solution
In a no solution problem the lines are parallel and will never intersect so the problem has no solution.
Infinitely Many
In an infinitely many problem the two lines lie on top of each other, that means that there is an infinite number of solutions.
Write a System
1. I made an equation using the money paid and then I made one for the t-shirts sold.
2. I used substitution to find x, then I plugged x back in to get y.
3. My answer was the coordinates I got from the equation.
Word Problems
1. I made two equations out of the data given, I made one using the money paid and the other using the amount of books purchased.
2. I used elimination to solve the system of equations an then, I simplified until I got the answer to x.
3. I plugged x back into the first equation to find what y is equal to.
4. My solution was (5,3), but the question asks for how many hardcover books she purchased. The answer is 5 because x represented hardcover books.
Graphing
1. I converted both equations to slope intercept. My starting equations were 2x+7y=14 and 5x+7y=-7. They converted to y=-2/7x+2 and y=-5/7x-1. Then I imputed them into the calculator and (-7,4).
When Do I Use Substitution?
Substitution is most helpful when one of the variables is already isolated in one of the two equations. For, example, x= 4y -2, and 2x+8y=20, the equation for x can be plugged in, to get the solution.
When Do I Use Elimination?
Elimination is most helpful when both the equations are in the same form. For example, -2x+10y= 5 and 2x+4y=8 can easily be added together with little amount of work required.
When Do I Use Graphing?
Graphing is most helpful when the equations are both in slope intercept form or y=mx+b. For example, y=6x+8 and y=2x+10, they can both be easily put in a calculator to graph.