5.4 - Writing and Solving Systems of Equations

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

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the same scenario.

Front

What does it mean if a system of equations has no solution?

Back

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

Front

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

Back

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

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then 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

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

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing the equations on a coordinate plane and identifying the point(s) of intersection.

Front

What is the importance of coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting the number of solutions.