System 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.

Front

What does it mean for a system of equations to have a unique solution?

Back

A unique solution occurs when the graphs of the equations intersect at exactly one point.

Front

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

Back

No solution occurs when the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

Infinitely many solutions occur when the equations represent the same line, meaning they intersect at every point on that line.

Front

How can you solve a system of equations graphically?

Back

To solve graphically, plot each equation on the same graph and identify the point(s) of intersection.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method for 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 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 do you determine the slope of a line from two points?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1) using two points (x1, y1) and (x2, y2).

Front

What is the graphical representation of the equations y = -x - 2 and y = x + 4?

Back

The graph of y = -x - 2 is a line with a negative slope, while y = x + 4 is a line with a positive slope. They intersect at the solution of the system.