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 another equation.

Front

How do you solve for y in the equation x = 3y?

Back

To solve for y, rearrange the equation: y = x/3.

Front

What is the first step in solving the system: x = 3y and 2x - y = 10?

Back

Substitute x = 3y into the second equation: 2(3y) - y = 10.

Front

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

Back

The solution is (10, -9).

Front

How do you check if (6, 2) is a solution to the system: x = 3y and 2x - y = 10?

Back

Substitute x = 6 and y = 2 into both equations to verify they hold true.

Front

What is the graphical interpretation of a system of equations?

Back

The graphical interpretation is the point(s) where the lines representing the equations intersect.

Front

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

Back

It means the lines are parallel and never intersect.

Front

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

Back

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

Front

How do you solve the system: 6x = y and 3y - 4x = 42?

Back

Substitute y = 6x into the second equation: 3(6x) - 4x = 42.