Solving Systems by Substitution

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 to solve a system of equations by substitution?

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the first step in solving a system of equations by substitution?

Back

The first step is to isolate one variable in one of the equations.

Front

If you have the equations y = 2x + 3 and 4x - y = 1, how would you start solving them by substitution?

Back

You would substitute y from the first equation into the second equation: 4x - (2x + 3) = 1.

Front

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

Back

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

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

Solve the system: y = -1x - 5 and 4x - 8y = 4. What is the solution?

Back

(-3, -2)

Front

Solve the system: x = 3y - 13 and 4x + 2y = 4. What is the solution?

Back

(-1, 4)

Front

Solve the system: x = -3y - 17 and 2x + 3y = -7. What is the solution?

Back

(10, -9)

Front

What is the substitution method used for?

Back

The substitution method is used to find the values of variables that satisfy all equations in a system.