System 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.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the elimination method in 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 variable.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the graphs of the equations intersect at one or more points.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the graphs of the equations are parallel and never intersect.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation shows the equations as lines on a coordinate plane, where the intersection point(s) represent the solution(s).

Front

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

Back

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

Front

What is a dependent system of equations?

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A dependent system has infinitely many solutions, meaning the equations represent the same line.

Front

What is the importance of the 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.

Front

How do you interpret word problems involving systems of equations?

Back

Identify the variables, set up equations based on the relationships described, and solve the system to find the values of the variables.