Quick check intro to systems

Front

What is a system of equations?

Back

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

Front

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

Back

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

Front

What is the graphical method for solving a system of equations?

Back

Plotting the equations on a graph and finding the point(s) where they intersect.

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

Back

(3,0)

Front

What is the substitution method in solving systems of equations?

Back

Solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

The system has at least one solution.

Front

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

Back

The system has no solutions.

Front

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

Back

(−2,−1)