Q: Can a graph be used to determine the number of solutions an equation has?

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Count the number of many times the graph intersects the x-axis. Each crossing point is a root of the equation.

The coordinates of every point on the graph, and no other points, are solutions of the equation.

There are an infinite number of equations that meet that requirement. One of them is y = x

A single equation in two variables is, for example. Its graph is a line, and every point on the line is a solution.

The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.

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Count the number of many times the graph intersects the x-axis. Each crossing point is a root of the equation.

Graph of an equation.

The coordinates of every point on the graph, and no other points, are solutions of the equation.

The X-Intercepts are the solutions. If you have an algebra calculator, you can usually find them by going to CALC>Zero>enter the left and right boundaries for each side.

If it is a straight line, then the equation is linear.

There are an infinite number of equations that meet that requirement. One of them is y = x

A single equation in two variables is, for example. Its graph is a line, and every point on the line is a solution.

The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.

When you graph the quadratic equation, you have three possibilities... 1. The graph touches x-axis once. Then that quadratic equation only has one solution and you find it by finding the x-intercept. 2. The graph touches x-axis twice. Then that quadratic equation has two solutions and you also find it by finding the x-intercept 3. The graph doesn't touch the x-axis at all. Then that quadratic equation has no solutions. If you really want to find the solutions, you'll have to go to imaginary solutions, where the solutions include negative square roots.

hi

It represents all solutions to the linear equation.

From the equation, the y intercept is simply determined by setting x = 0. The x intercept(s) are generally much harder to find: you will need to find the solutions of y = 0 [or f(x) = 0]. From the graph the intercepts are the coordinates of the points at which the graph crosses the axes.