Systems of Equations 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 set of values that satisfy all equations in the system.

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 reflect the problem's constraints.

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution in common.

Front

What does it mean for two equations to be independent?

Back

Two equations are independent if they represent different lines that intersect at exactly one point.

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

Front

How do you solve a system of equations graphically?

Back

Graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

Front

What is elimination in solving systems of equations?

Back

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

Front

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

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection and solution.

Front

How can you check the solution of a system of equations?

Back

Substitute the solution values back into the original equations to verify that both equations are satisfied.