System of Equation 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 express them in a system.

Front

What does it mean to solve a system of equations?

Back

To find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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.

Front

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

Back

Substitute the values of the variables back into the original equations to verify that they hold true.

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b.

Front

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

Back

Coefficients represent the relationship between variables; they determine the slope and position of the lines in a graph.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

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