Systems Review

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations by elimination?

Back

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

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the graphs of the equations, representing the solution(s) to the system.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do 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 satisfied, the point is a solution.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it moves (positive or negative) as x increases.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x=0.

Front

How can you graph a system of inequalities?

Back

Graph each inequality as a line, then shade the appropriate region that satisfies the inequality.