Solving Linear Systems of Equations

Front

What is a linear system of equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What does it mean if two lines intersect at a point on a graph?

Back

The coordinates of the intersection point represent the solution to the system of equations.

Front

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

Back

The 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

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means the system has no solution because the lines never intersect.

Front

What does it mean if two lines are coincident?

Back

It means the system has infinitely many solutions because the lines lie on top of each other.

Front

How can you solve a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point of intersection.

Front

What is the substitution method for solving linear systems?

Back

Solve one equation for one variable and substitute that expression into the other equation.