Solving Systems with Substitution

Front

What does 'solution to a system of equations' mean?

Back

It's the point that solves both equations at the same time.

Front

Solve the following systems of equations using substitution: 5x - 2y = 3, y = 2x

Back

(3, 6)

Front

Solve: y=8x+1, y=6x+3

Back

(1, 9)

Front

How many solutions does the graph have?

Back

Infinite solutions

Front

What is the solution to this system? 2x + 3y = 4, y= 5x - 27

Back

(5,-2)

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 the other equation.

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 does it mean if two lines are the same in a system of equations?

Back

It means there are infinite solutions, as every point on the line is a solution.

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 first step in solving a system of equations using substitution?

Back

Isolate one variable in one of the equations.