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

How do you isolate a variable in an equation?

Back

You manipulate the equation to get the variable on one side by itself.

Front

What is the first step in solving the system: 6x = y and 3y - 4x = 42?

Back

Substitute y from the first equation into the second equation.

Front

What is the solution to the system of equations: y = -4x + 5 and y = 3x - 16?

Back

(3, -7)

Front

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

Back

It means that the point is the solution to both equations.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the values of the variables that satisfy both equations.

Front

How can 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 solution to the system: 3x + 3y = 3 and y = 3x + 5?

Back

(3, 18)