Solving Systems of Linear Equations

Front

What is a system of linear equations?

Back

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

Front

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

Back

It means that the point satisfies all equations in the system.

Front

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

Back

Substitute the point's coordinates into each equation; if all equations are true, it's a solution.

Front

What is the graphical representation of a system of linear equations?

Back

The intersection point(s) of the lines representing the equations.

Front

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

Back

The system has no solution because the lines never intersect.

Front

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

Back

The system has infinitely many solutions because the lines are the same.

Front

What is the substitution method for solving systems of equations?

Back

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

Add or subtract equations to eliminate one variable, making it easier to solve.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3) is the solution.

Front

How do you graph a linear equation?

Back

Find two or more points that satisfy the equation and plot them on a coordinate plane.