Solving Systems of Equations

The video tutorial explains how to find two numbers given their sum and product. It sets up equations for the sum and product, uses substitution to solve the equations, and factors a quadratic equation to find the solutions. The tutorial concludes by verifying the solutions graphically, confirming that the two numbers are 7 and 19.

What is the sum of the two numbers we are trying to find?

• 24

• 27

• 25

• 26

Tags

CCSS.8.EE.A.2

What is the product of the two numbers we are trying to find?

• 130

• 131

• 132

• 133

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

• Substitution

• Matrix

• Elimination

• Graphing

What is the equation formed after substituting Y in the second equation?

• X(26 - X) = 133

• X + Y = 26

• X(26 + X) = 133

• X - Y = 26

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What type of equation is formed after substitution?

• Cubic

• Quadratic

• Exponential

• Linear

Tags

CCSS.HSA-REI.B.4B

What are the factors of the quadratic equation?

• (X - 20)(X - 6)

• (X - 21)(X - 5)

• (X - 19)(X - 7)

• (X - 18)(X - 8)

Tags

CCSS.HSA-REI.B.4B

What are the possible values of X after factoring?

• 21 and 5

• 19 and 7

• 18 and 8

• 20 and 6

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

If X is 19, what is the value of Y?

• 9

• 8

• 7

• 6

If X is 7, what is the value of Y?

• 18

• 19

• 20

• 21

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

What is the final solution for the two numbers?

• 6 and 20

• 7 and 19

• 8 and 18

• 9 and 17

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6