Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the lines represented by the equations are parallel and never intersect.

Front

What is the point of intersection in a system of equations?

Back

The point of intersection is the solution to the system, where the values of the variables satisfy all equations in the system.

Front

How do you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines (or curves) on a coordinate plane, where the intersection points represent the solutions.

Front

What is the solution to the system: 2x + 3y = 6 and x - y = 1?

Back

The solution is (3, 0).

Front

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

Back

Infinitely many solutions occur when the equations represent the same line, meaning every point on the line is a solution.

Front

What is the first step in solving the equation 13y - 18 = -5y + 36?

Back

The first step is to combine like terms by adding 5y to both sides, resulting in 18y - 18 = 36.

Front

What is the equation to find when two products cost the same?

Back

The equation is set up by equating the total costs of the two products, e.g., 150 + 24x = 180 + 20x.