6.4 & Story 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 that 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 that the equations represent the same line, so every point on the line is a solution.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If both equations are satisfied, the point is a solution.

Front

What is the graphical representation of a system of equations with one solution?

Back

Two lines that intersect at exactly one point.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations and manipulate them to eliminate one variable.

Front

What are the coefficients in a linear equation?

Back

The numerical factors that multiply the variables in the equation.

Front

What does the term 'application-based question' refer to in mathematics?

Back

Questions that require applying mathematical concepts to real-world scenarios.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, representing the value of y when x is zero.