Unit 5- Systems of Equations Review for Test

Front

What is a system of linear equations?

Back

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

Front

What does it mean if two linear equations represent the same line?

Back

If two linear equations represent the same line, it means they have infinitely many solutions, as every point on the line is a solution.

Front

What is the solution to a system of linear equations that intersect at one point?

Back

The solution is exactly one point, which is the coordinates of the intersection.

Front

What is the solution to a system of linear equations that are parallel?

Back

If the equations are parallel, there is no solution, as they never intersect.

Front

How do you find the solution to a system of equations graphically?

Back

You graph both equations on the same coordinate plane and identify the point(s) where they intersect.

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 if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into both equations. If both equations are true, the point is a solution.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

The coefficients determine the slope and position of the line on the graph.

Front

How do you solve a system of equations using substitution?

Back

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