Solving Systems of Equations by substitution (easy)

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations by substitution?

Back

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

Front

What is the solution to the system of equations 4x + 2y = -6 and y = -8?

Back

(2.5, -8)

Front

What is the solution to the system of equations -2x - 2y = 16 and y = -8?

Back

(0, -8)

Front

What does the graph of a system of equations with exactly one solution look like?

Back

Two lines intersecting at one point.

Front

What is the solution to the system of equations -5x - 4y = -9 and y = 6?

Back

(-3, 6)

Front

What is the solution to the system of equations y = 3x + 9 and y = -6?

Back

(-5, -6)

Front

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

Back

It means there is no solution, as the lines never intersect.

Front

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

Back

It means there are infinitely many solutions, as every point on the line is a solution.

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.