# 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. |

## 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.

## 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.

## 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.