Det här är en översatt version av sidan Varför är skärningspunkten lösningen till ett ekvationssystem *Why*. Översättningen är till 100% färdig och uppdaterad.

# Why is the point of intersect the solution for a system of equations?

The solution to the system of equations $\begin{cases}y=x+1 \\ y=3-x \end{cases}$ is the values of $x$ and $y$which solve both equations $y=x+1 \quad \text{ och } \quad y=3-x$ at the samt time. Every equation has an infinite number of solutions. The table shows a few pair a whole numbers which solve the first equation.

$y=x+1$
$\phantom{xx} x \phantom{x}$ $\phantom{x} y \phantom{xx}$
$1$ $2$
$2$ $3$
$3$ $4$
$\vdots$ $\vdots$

You could say that all these number pairs lie along the straight line $y=x+1.$ Here are a few shown, but in reality there are an infinite number of them.

In the same way, you can represent all the solutions for the equation $y=3-x$ by using points along the line $y=3-x.$ Where can you find the number pair that solves both equations? Right where the lines intersect each other!

If you try putting $x=1$ and $y=2$ into both equations, you will see that both agree.