Flashcard 6-1: System of linear equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

Front

How do you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

What is the y-intercept of a linear equation?

Back

The point where the line crosses the y-axis, represented as (0, y).

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

How can you determine the slope from an equation in slope-intercept form?

Back

In the equation y = mx + b, m represents the slope.

Front

What is the zero of a function?

Back

The x-value(s) where the function equals zero, also known as the x-intercept.

Front

What does it mean for two lines to be intersecting?

Back

They cross at one point, indicating a unique solution to the system of equations.

Front

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

Back

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

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.