Solving Systems of Equations with Substitution

What is the first step in the substitution method for solving systems of equations?

• Substitute one variable into the other equation

• Solve for one variable in one equation

• Combine like terms

• Graph the equations

In the substitution method, after solving for one variable, what should you do next?

• Check the solution in both equations

• Solve for the same variable in the other equation

• Substitute the solved value into the other equation

• Graph the solution

What is the correct order of steps in the substitution method?

• Solve for one variable, substitute, solve for the second variable, check the solution

• Solve for one variable, substitute, solve for the second variable

• Solve for one variable, substitute, solve for the second variable, substitute back

• Substitute, solve for one variable, solve for the second variable, check the solution

What does it mean to solve for a variable in one of the equations?

• To combine like terms first

• To substitute the variable into the other equation immediately

• To isolate the variable on one side of the equation

• To graph the equation

What should you do if you get a variable by itself equals a number?

• Check the solution in both equations

• Start over with a different variable

• Graph the equation

• Substitute it back into one of the original equations

How do you solve for a variable when its coefficient is a fraction?

• Subtract the fraction from both sides

• Multiply by the reciprocal of the fraction

• Add the fraction to both sides

• Divide by the fraction

When combining like terms, what is crucial to remember?

• To ensure you are only combining terms with the same variable

• To multiply the variables

• To add the coefficients of the variables

• To always divide by the coefficient of the variable

When solving a system of equations using substitution, what indicates that you have infinitely many solutions?

• When you cannot combine like terms

• When variables cancel out leaving a true statement

• When you solve for a variable and get a number

• When you get a false statement

What does it mean if, after substituting and simplifying, you end up with a statement that is not true?

• The equations are not linear

• The system has no solution

• The system has infinitely many solutions

• The system has one unique solution

In the substitution method, how can you tell if an equation has no solution?

• If substituting one variable makes the other variable disappear

• If you end up with a variable equal to a number

• If you get a false statement after simplifying

• If the variables cancel out leaving a true statement