Substituition

Front

What is substitution 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 to find the values of the variables.

Front

How do you solve for y in the equation x = 7 - 2y?

Back

Rearranging gives y = (7 - x)/2.

Front

What is the first step in solving the system: x = 7 - 2y and 2x + y = 5?

Back

Substitute x from the first equation into the second equation.

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 = 4x + 3 and 2x - 3y = 21?

Back

The solution is (-3, -9).

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 solution to the system: y = 2x and 5x - 2y = 3?

Back

The solution is (3, 6).

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, and every point on the line is a solution.

Front

What is the solution to the system: y = 3 - x and 3y + x = 5?

Back

The solution is (2, 1).