Writing Systems of Equations Through Word Problems

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 set them equal to each other.

Front

What does it mean for two lines to intersect on a graph?

Back

It means that the two equations have a common solution, which is the point where both equations are true.

Front

What is the significance of the solution to a system of equations in a word problem?

Back

The solution represents the values of the variables that satisfy all equations in the system, often corresponding to a real-world scenario.

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 they hold true.

Front

What is the graphical method of solving a system of equations?

Back

Plot both equations on a graph and identify the point of intersection.

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means that the system has no solution, as the lines will never intersect.

Front

What is the substitution method for solving systems of equations?

Back

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

Front

What is the elimination method for solving systems of equations?

Back

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

Front

How do you interpret the slope of a line in a word problem context?

Back

The slope represents the rate of change between the two variables in the context of the problem.