Systems of Linear Equations

Front

What is the solution to the system of linear equations represented by the point (1,3)?

Back

The solution is the point where the two lines intersect, which is (1,3).

Front

How many solutions does a system of linear equations have if the lines are parallel?

Back

No solutions.

Front

How many solutions does a system of linear equations have if the lines are coincident?

Back

Infinitely many solutions.

Front

What is the Slope Intercept Form of a Linear Equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What do you call lines whose graphs do not intersect?

Back

Parallel Lines.

Front

What does the slope (m) represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept is the value of y when x = 0, represented by b.

Front

What does it mean if a system of equations has one solution?

Back

It means the lines intersect at exactly one point.

Front

What is the graphical representation of a system of equations with no solutions?

Back

The lines are parallel and never intersect.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The lines are coincident, meaning they lie on top of each other.