Flashcard 6-6: 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 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 equations has no solution?

Back

If a system has no solution, it means the lines are parallel and will never intersect. This indicates that the equations represent different lines with the same slope.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

If a system has infinitely many solutions, it means the equations represent the same line, and every point on that line is a solution.

Front

What is the constant of variation in a direct variation equation?

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

If y varies directly with x and y = 7 when x = 14, what is the constant of variation?

Back

Front

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

Back

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

Front

How do you find the slope of a line given two points?

Back

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form y = mx + b.

Front

What is the graphical representation of the equation y = 2x + 3?

Back

The graph is a straight line with a slope of 2 and a y-intercept at (0, 3).