Question

The graph below shows a system of equations:

Draw a line labeled y equals minus x plus 5 by joining the ordered pairs 0, 5 and 5, 0. Draw a line labeled y equals x minus 1

The x-coordinate of the solution to the system of equations is____

Answer 1

If you graph the two lines they cross at (3,2). This means the x coordinate at the solution is 3.

Answer 2

`x=3`

Explanation:

The graph is shown in the image attached.

The given equations are:

`\left \{ {{y=-x+5} \atop {y=x-1}} \right.`

The solutions of this system represent the point that both lines have in common, which is also represented in the graph.

Always a system of equations represents the intercepting points between those curves.

Notice that if we multiply one equation by -1, we could eliminate one variable and find the value of the other one:

`\left \{ {{y=-x+5} \atop {-y=-x+1}} \right.\\0=-2x+6\\2x=6\\x=3`

Then, we replace this value in one equation to find the other value:

`y=-x+5=-3+5=2`

Therefore, the solution is the point
`(3,2)`

So, the x-coordinate of the solution to the system of equations is
`x=3`