This week in math 10 I learned what systems of lines are and how to find the point at were they cross by using graphing and substitution. Systems of lines are when given 2 equations and you have to find were they cross.

**Using Graphing**

To find were they cross you need to rearrange the equation into slope y intercept form (y=mx+b). When doing this you need to make sure that the y is positive and by itself with no coefficient and made sure when putting something on the other side of the equals sign.

From looking at just the rearranged equations you can tell how many solutions (how many points the two lines will cross). If the equations have same slope but a different y intercept, they are parallel so they will never touch, which means there is no solutions. If the slope is different the lines will cross and there will be one solution. if both the slope and y intercept are the same then there is a lot of solutions because they are on top of each other.

**Using Substitution**

When given two line equations substitution is another way to find a solution. When looking at the equations you need to choose one of the variables and isolate it.

Then put the new rearranged equation into the other one that you did not rearrange. Next you next to solve for the single variable. Then depending on which you isolated first you now either have the x or y value.

With the variable you have plug that into the rearranged equation to find the other missing value.

**Verifying Solution**

Once you have the two coordinates of where the lines cross there is a way to check your answer by plugging in the x and y values into the equations if the numbers on both sides of the equals sign are equal for both equations then you know you have the right answer.