Systems 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.

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 where they intersect. This point is the solution.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

The solution is (3, 0).

Front

What is the graphical representation of the inequality y > -1/5x - 1/2?

Back

The graph is a dashed line representing the equation y = -1/5x - 1/2, with the area above the line shaded.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the coordinates of the point into each equation. If the point satisfies all equations, it is a solution.

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

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

Back

An inconsistent system has no solution, meaning the lines representing the equations are parallel and never intersect.

Front

What is the solution to the system of inequalities: y ≤ -2x + 6 and y > -1/4x - 3?

Back

The solution is the region where the area below the line y = -2x + 6 and above the line y = -1/4x - 3 overlap.