17Summary

Intersection point

You learned in this course what an intersection point is and how to read it off.

Linear system of equations

You now know that a linear system of equations consists of two (or more) linear equations. These equations depend on the same variables (usually denoted $x$ and $y$).

• Number the equations with Roman numerals so that you don't lose track of them.

• You are looking for the solution of the linear system of equations, which is the point $(x|y)$ at which all equations yield true statements. That means: If you plugthe point into the equations, something like $7=7$ comes out. (Hint: Plug $x = 2$ and $y=0$ into the above system).

• If you transform all equations of the sysetm into straight line equations of the form $y=m\cdot x+t$, the solution of the equation system is exactly the intersection of these straight lines.

Elimination by equating coefficients

If you cannot read off the intersection or cannot read it off precisely enough, you can calculate it. To do this, you use the elimination by equating coefficients, which gives you the solution of the system in three steps:

1. Equating: Set equal equations $\mathrm{I}$ and $\mathrm{II}$ .

2. Solving: Solve the resulting equation for one variable.

3. Plugging in: By substituting into the equation $\mathrm{I}$ or $\mathrm{II}$ you get the value of the other variable.