Flashcard 6: System of linear equations

Front

What is a system of linear equations?

Back

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

Front

How do you solve a system of linear equations by graphing?

Back

To solve by graphing, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect. This point is the solution to the system.

Front

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

Back

It means that the lines representing the equations are parallel and will never intersect.

Front

What is the constant of variation in direct variation?

Back

The constant of variation is the ratio of y to x in a direct variation equation, expressed as y = kx, where k is the constant.

Front

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

Back

You can use substitution or elimination methods to find the values of the variables that satisfy all equations in the system.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

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

Front

What does it mean for two lines to be coincident?

Back

Coincident lines are lines that lie on top of each other, meaning they have infinitely many solutions as they represent the same line.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the line.