System of Equations--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 the context of solving 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 identify which equation to solve for a variable in substitution?

Back

Choose the equation that is easiest to manipulate, typically the one that has a coefficient of 1 or -1 for one of the variables.

Front

What is the first step in the substitution method?

Back

Find the equation that is solved for the single variable.

Front

Solve the system using substitution: y = 2x, 5x - 2y = 3. What is the solution?

Back

(3, 6)

Front

Solve the system using substitution: y = 8x + 1, y = 6x + 3. What is the solution?

Back

(1, 9)

Front

What is the solution to the system of equations: y = 8x + 2, y = -x - 7?

Back

(-1, -6)

Front

What is the substitution method used for?

Back

The substitution method is used to find the values of variables that satisfy all equations in a system.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into the original equations to see if both equations are satisfied.