Question

Sometimes the best way to solve an equation, a system of equations, or a system of inequalities is to look at a graph of the equation or the system. Finding solutions on graphs is different from using algebraic properties to solve for a variable, but it gives the same results. For each of the three graphs, describe how and why the graph shows the solutions of the equation or system of equations or inequalities.

Answer 1

When we solve a system of equations, we are looking for the points at which both graphs intercept. Solving a system of equations sometimes can be hard, and you should use other methods -Like numeric methods- to solve it. That's why sometimes is easier to look at the graph of the equation.

To solve a equation, system of equations or a system of inequalities, we should graph each of the equations separatedly, and the result will be the point at which the functions intercept or a single function intercepts the x-axis.

If the function does not intercept another function or the x-axis, then it has no real roots. The number of solutions an equation can have, will depend on the degree of the equation.