Solving pairs of linear equations in two variables

Front

What is a linear equation in two variables?

Back

An equation that can be written 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 two lines to intersect?

Back

It means that the two lines have exactly one point in common, which is the solution to the system of equations.

Front

What is the solution to a system of linear equations?

Back

The point (x, y) where the two lines intersect, representing the values of the variables that satisfy both equations.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What does 'no solution' mean in the context of linear equations?

Back

It means that the lines are parallel and do not intersect, indicating that there are no values of x and y that satisfy both equations.

Front

What does 'infinitely many solutions' mean?

Back

It means that the two equations represent the same line, and every point on that line is a solution.

Front

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

Back

Substitute the x and y values of the point into both equations. If both equations are true, then the point is a solution.

Front

What is the substitution method for solving systems of equations?

Back

A method where you 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

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

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