Systems of Equations/ Word Problems

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means the equations represent parallel lines that 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, so every point on the line is a solution.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the graphical representation of intersecting lines?

Back

It shows that the system has one unique solution where the lines cross.

Front

If y = mx + b, what do m and b represent?

Back

m is the slope of the line, and b is the y-intercept.

Front

How do you solve a system of equations using substitution?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable, making it easier to solve.

Front

What is the first step in solving a word problem involving a system of equations?

Back

Define the variables and write the equations based on the problem's context.

Front

What does the term 'dependent' mean in relation to systems of equations?

Back

Dependent means that the equations represent the same line, leading to infinitely many solutions.