Systems of equations

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 graphs of the equations intersect.

Front

What does it mean to solve a system of equations graphically?

Back

It means to find the point(s) where the graphs of the equations intersect, which represents the solution to the system.

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the first step in using the elimination method?

Back

Identify which variable to eliminate and manipulate the equations accordingly.

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

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

Back

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

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Front

How can you check your solution to a system of equations?

Back

Substitute the solution back into the original equations to see if it satisfies both equations.

Front

What is the graphical representation of the solution (1, 3)?

Back

It is the point where the x-coordinate is 1 and the y-coordinate is 3 on the graph.

Front

What is the solution to the system of equations 2x - 3y = 6 and 7x - 3y = -9?

Back

(-3, -4) is the solution.