Systems of Equations-Substitution Method

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What is the substitution method in solving systems of equations?

Back

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 y = 4x + 1?

Back

Substitute the value of x into the equation to find the corresponding value of y.

Front

If 4x + 1 = y and 2x + 3 = y, how do you find x?

Back

Set the two equations equal to each other: 4x + 1 = 2x + 3.

Front

What does it mean if two equations intersect at a point on a graph?

Back

It means there is a unique solution to the system of equations at that point.

Front

What is the first step in using the substitution method?

Back

Solve one of the equations for one variable in terms of the other.

Front

If you have y = 2x + 5, how can you find y when x = 3?

Back

Substitute x = 3 into the equation: y = 2(3) + 5 = 11.

Front

What is the solution to the system of equations 2x + 7 = y and 3x + 2y = 35?

Back

The solution is (3, 13).

Front

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

Back

It means the lines representing the equations are parallel and never intersect.

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.