Exploring Adding and Subtracting Rational Expressions

What is the primary goal when solving systems of equations?

• To determine if the equations are parallel

• To rewrite the equations in a different format

• To find the values of x and y where the equations intersect

• To graph the equations on a coordinate plane

What is the first step in the substitution method?

• Multiply both equations by a common factor

• Graph the equations to find the intersection point

• Solve for either x or y in one of the equations

• Substitute one equation into the other

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

• They intersect at infinitely many points

• They do not intersect at any point

• They intersect at exactly one point

• They form a right angle at the intersection point

What is the result of solving a system of equations where both equations are identical?

• Infinitely many solutions

• No solution

• Exactly one solution

• Two distinct solutions

In the substitution method, what do you do after solving for x or y?

• Solve for the other variable in the same equation

• Substitute the solved value into the other equation

• Graph the solution on a coordinate plane

• Check the solution by plugging it back into the original equations

What indicates that you have correctly solved a system of equations using the substitution method?

• You prove that the two equations are equivalent

• You find the values of both x and y that satisfy both equations

• You find the value of y only

• You find the value of x only

When solving using the substitution method, why might you choose to solve for y first?

• It is always easier to solve for y

• Solving for x is not allowed in the substitution method

• Solving for y might be simpler based on the equation's structure

• It is a requirement of the substitution method

What should you do if your solution for a system of equations using the substitution method results in a decimal?

• Recheck your calculations; the answer should be a whole number

• Assume the equations do not intersect

• Graph the equations to find the exact intersection point

• Consider the solution as correct; decimals are acceptable

How can you verify your solution to a system of equations solved by substitution?

• By checking if the solution forms a straight line on a graph

• By solving the system using another method for comparison

• By substituting the values back into both original equations

• By asking a peer to solve the same system

Why is it important to practice solving systems of equations using the substitution method?

• It improves problem-solving skills and mathematical thinking

• It is required for all algebra courses

• It helps in understanding complex algebraic expressions

• It is the only method to solve systems of equations