Flash Cards: Pair of Linear Equations in Two Variables

A pair of linear equations consists of two equations that relate two variables, often represented as ax + by + c = 0.

A consistent pair of linear equations has at least one solution, meaning the lines intersect.

A dependent pair has infinitely many solutions, represented by coincident lines.

Linear equations are represented as lines on the Cartesian plane, with their intersections indicating solutions.

When the lines intersect at exactly one point, the pair is consistent with a unique solution.

Use the ratios a1/a2, b1/b2, c1/c2: If they are equal, lines are parallel or coincident; if not, they intersect.

For equations x + 3y = 6 and 2x - 3y = 12, the intersection shows the solution (6,0).

The standard form is expressed as Ax + By + C = 0, where A, B, C are constants.

A technique where one variable is eliminated by adding or subtracting equations to simplify solving.

A technique where one equation is solved for one variable, and then substituted into the other equation.

Translate the words into equations, like for costs: 3x + 4y = total spent and y = 1/2x.

Confusing the signs during addition/subtraction of equations can lead to incorrect solutions.

The intersection point (x, y) is the solution to the pair of linear equations.

Coincident lines are lines that lie on top of each other, representing infinitely many solutions.

Parallel lines have the same slope but different y-intercepts, indicating no intersection.

Find two or more points that satisfy the equations and draw lines through them.

You can divide equations by common factors to make calculations easier.

A system is a set of equations with the same variables that can be solved together.