Solving Systems using 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 substitution mean in solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

How do you solve for y in the equation x = 5y + 2?

Back

Rearranging gives y = (x - 2)/5.

Front

What is the first step in solving the system x = 5y + 2 and 4y = x?

Back

Substitute x from the first equation into the second equation.

Front

What is the solution to the system x = 7 - 2y and 2x + y = 5?

Back

The solution is (1, 3).

Front

How do you check if a solution is correct for a system of equations?

Back

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

Front

What is the solution to the system y = 5x - 7 and 3x + 2y = 12?

Back

The solution is (2, 3).

Front

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

Back

If two lines are parallel, the system has no solution because the lines never intersect.

Front

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

Back

The solution is (4, 5).

Front

What is the solution to the system y = 11 and y + 4x = 35?

Back

The solution is (4, 11).