Solutions for Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean if a system of equations has one solution?

Back

The lines represented by the equations intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines represented by the equations are the same line, overlapping each other.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are true, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on a coordinate plane.

Front

What is the significance of the slopes of two lines in a system of equations?

Back

If the slopes are equal and the y-intercepts are different, there is no solution. If the slopes are different, there is one solution.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the solution of a system of equations graphically?

Back

Plot both equations on a graph and identify the point(s) where they intersect.

Front

What is substitution method in solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.