Solving Systems using Substitution

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 does it mean to solve a system of equations using substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the first step in solving a system of equations by substitution?

Back

Isolate one variable in one of the equations.

Front

If y = 2x + 1, what is y when x = 3?

Back

y = 2(3) + 1 = 7.

Front

What is the solution to the system of equations: y = 3x - 8 and y = 4 - x?

Back

(3, 1).

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 graphical representation of a system of equations?

Back

The point where the graphs of the equations intersect represents the solution.

Front

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

Back

It means there is no solution, as the lines never intersect.

Front

What is the solution to the system of equations: 5x + 4y = -14 and y = -7x - 15?

Back

(-2, -1).

Front

What is the solution to the system of equations: y = 2x + 1 and y = 4x - 1?

Back

(1, 3).