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 point(s) where the equations intersect.

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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 (they intersect at one or more points).

Front

What does it mean for two equations to be independent?

Back

Two equations are independent if they have exactly one solution (they intersect at one point).

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they have infinitely many solutions (they represent the same line).

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.

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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 importance of checking your solution in a system of equations?

Back

Checking your solution ensures that the values satisfy all equations in the system, confirming they are correct.

Front

How can you identify the variables in a word problem?

Back

Look for quantities that change or are unknown, and assign a variable to each of these quantities.