Mathematics Flashcard

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 solve a system of equations using substitution?

Back

To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the equations do not intersect at any point.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you find the y-value of a solution in a system of equations?

Back

To find the y-value, substitute the x-value from the solution into one of the original equations.

Front

What is the substitution method in solving equations?

Back

The substitution method involves solving one equation for one variable and substituting that value into another equation.

Front

What is the elimination method in solving equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.