Solving a System of Equations

The video tutorial explains how to solve a problem involving the sum and difference of two numbers. It begins by setting up a system of equations using variables for the unknown numbers. The elimination method is used to solve the equations, leading to the discovery of the first number. Back substitution is then performed to find the second number, confirming that the sum is 52 and the difference is 38.

What is the sum of the two numbers mentioned in the problem?

• 38

• 52

• 90

• 45

What is the difference between the two numbers in the problem?

• 7

• 52

• 90

• 38

What variable is assigned to the first number?

• X

• Y

• Z

• A

What is the first equation formed from the problem statement?

• X + Y = 90

• X + Y = 52

• X - Y = 38

• X - Y = 7

Which method is used to solve the system of equations in the video?

• Matrix

• Elimination

• Graphing

• Substitution

What happens to the Y terms when the two equations are added?

• They become negative

• They remain unchanged

• They cancel out

• They double

What is the value of X after solving the equation?

• 38

• 45

• 7

• 52

What is the next step after finding the value of X?

• Solve for Z

• Check the solution

• Graph the equations

• Perform back substitution

What is the value of Y after back substitution?

• 38

• 45

• 52

• 7

Why are the numbers 45 and 7 correct solutions?

• Their sum is 52 and difference is 38

• Their sum is 38

• Their sum is 90

• Their difference is 52