Solve Systems by Substitution

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 first step in solving a system by substitution?

Back

Isolate one variable in one of the equations.

Front

If x + 2y = 2 and x = -4y + 2, what is the value of y?

Back

y = 0.

Front

What is the solution to the system: 5x + 4y = -14 and y = -7x - 15?

Back

(-2, -1).

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What is the solution to the system: y = 2x - 11 and -3y = -6x - 15?

Back

No solution (parallel lines).

Front

How do 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.

Front

What is the graphical representation of a system of equations?

Back

It is the point(s) where the lines of the equations intersect.

Front

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

Back

It means the equations represent the same line.