Skill: Determine whether an ordered pair solves a system of equations

To determine whether an ordered pair solves a system, substitute the $x$-coordinate and $y$-coordinate into both equations. The pair is a solution only if both equations are true.

Consider the system:

$$\begin{cases} y=2x-1\\ x+y=5 \end{cases}$$

Check whether $(2,3)$ is a solution.

1. Identify the coordinates: $x=2$ and $y=3$.

2. Substitute into the first equation:

$$y=2x-1$$ $$3=2(2)-1$$ $$3=4-1$$ $$3=3$$

The first equation is true.

3. Substitute into the second equation:

$$x+y=5$$ $$2+3=5$$ $$5=5$$

The second equation is also true.

Since $(2,3)$ makes both equations true, $(2,3)$ is a solution to the system. Graphically, this means $(2,3)$ is the point where the two lines intersect.