Solving Systems using Substitution

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you solve for y in the equation x = 3y + 1?

Back

Rearranging gives y = (x - 1)/3.

Front

What is the first step in using the substitution method?

Back

Identify one equation to solve for one variable.

Front

Given the equations y = -5x and x + 3y = 28, how do you find the value of x?

Back

Substitute y = -5x into the second equation and solve for x.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

Solve the system using substitution: x = 3y, 2y + x = -15. What is the solution?

Back

(-9, -3) is the solution.

Front

What is the solution to the system 8x + 4y = 12 and y = -2x + 3?

Back

Infinitely many solutions.

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.

Front

What is the solution to the system x = 3y + 1 and 2x + 4y = 12?

Back

(4, 1) is the solution.