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 of equations by substitution?

Back

Isolate one variable in one of the equations.

Front

If you have the equations y = 2x - 11 and -3y = -6x - 15, what is the first step to solve them by substitution?

Back

Substitute y from the first equation into the second equation.

Front

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

Back

It means there is no solution to the system because the lines never intersect.

Front

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

Back

The solution is (2, 0).

Front

What is an infinitely many solutions scenario in a system of equations?

Back

It occurs when the two equations represent the same line.

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.

Front

What is the substitution method used for?

Back

To find the values of variables that satisfy all equations in a system.

Front

What does it mean to isolate a variable?

Back

To rearrange an equation so that the variable is on one side and all other terms are on the other.