linear Equations in two Variables

Front

What is a linear equation in two variables?

Back

A linear equation in two variables is an equation that can be expressed in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

Front

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

Back

A pair of linear equations is consistent if there is at least one solution, meaning the lines represented by the equations intersect at one point or are coincident.

Front

What are the possible outcomes for a system of linear equations?

Back

1. One solution (intersecting lines) 2. No solution (parallel lines) 3. Infinitely many solutions (coincident lines)

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

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

Back

The slope-intercept form is 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 (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be coincident?

Back

Two lines are coincident if they lie on top of each other, meaning they have the same slope and y-intercept.

Front

What is the graphical representation of a system of equations with no solution?

Back

The graphical representation is two parallel lines that never intersect.

Front

How do you solve a system of equations using substitution?

Back

To solve using substitution, solve one equation for one variable and substitute 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 other.