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 to solve a system of equations using substitution?

Back

It means to solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

What is the purpose of using a solid line when graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (for ≤ or ≥).

Front

What is the purpose of using a dashed line when graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (for < or >).

Front

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

Back

Substitute the point's coordinates into both equations; if both equations are true, the point is a solution.

Front

What is the solution to the system of equations: x - 2y = 2 and 3x + 4y = 3?

Back

(1.4, -0.3)

Front

What is the solution to the system of equations: y = -x + 5 and y = 2x - 7?

Back

(4, 1) is a solution.