Unit 5 Systems Retest

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all equations true simultaneously.

Front

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

Back

Substitute the coordinates of the point into each equation. If all equations are satisfied, the point is a solution.

Front

What is the method of substitution in solving systems of equations?

Back

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

Front

What is the method of elimination in solving systems of equations?

Back

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

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Two lines are parallel if they have the same slope and will never intersect, meaning there is no solution to the system.

Front

What does it mean for two lines to be coincident in the context of systems of equations?

Back

Two lines are coincident if they lie on top of each other, meaning there are infinitely many solutions to the system.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines representing the equations on a coordinate plane.

Front

How can you find the y-coordinate of the solution to a system of equations?

Back

You can find the y-coordinate by solving the system of equations for y after determining the x-coordinate.

Front

What is the significance of the y-intercept in a linear equation?

Back

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

Front

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

Back

The slope is a measure of the steepness of the line, calculated as the change in y over the change in x (rise/run).