Systems of Equations - Review

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the graphs of the equations are parallel lines, meaning they never intersect.

Front

What is the graphical representation of intersecting lines in a system of equations?

Back

Intersecting lines represent a system of equations that has exactly one solution, which is the point of intersection.

Front

How do you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, which can be either one solution (intersecting lines) or infinitely many solutions (coincident lines).

Front

What is the solution to the system of equations 2x + 3y = 6 and x - y = 1?

Back

The solution is (3, 0).

Front

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

Back

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

Front

How can you determine the number of solutions in a system of equations by comparing slopes?

Back

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

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point where the line crosses the y-axis.