Solving 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 for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

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

Back

It means the equations represent parallel lines that never intersect.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How can you solve a system of equations using the substitution method?

Back

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

Front

How can you solve a system of equations using the elimination method?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

The solutions are represented by the points where the graphs of the equations intersect.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What is the slope of the line represented by the equation y = mx + b?

Back

The slope is represented by 'm' in the equation.

Front

What does the y-intercept represent in a linear equation?

Back

It is the point where the line crosses the y-axis, represented by 'b' in the equation y = mx + b.