Question

In the following exercises, solve the system of equations by using graphing.

$x+y=2,x=y^2$

Short answer

The solution of the system is$(1,1)\mathrm{and}(4,-2)$.

Step-by-step solution

Step 1. Given Information

The given system of equations is$x+y=2,x=y^2$

Step 2. Graph the Functions

• Plot the graphs of $\begin{array}{rcl}x+y& =& 2\mathrm{and}x=y^2\end{array}$on the same graph.

• The blue line represents the first equation and the red line represents the second equation of the system.

Step 3. Determine the point of intersection

• From the graph, it is observed that the functions intersect at $(1,1)\mathrm{and}(4,-2)$
• So, the solution of the system is$(1,1)\mathrm{and}(4,-2)$.