1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Volgvan
2 years ago
7

Solve the following system of equations algebraically: y = x2 - 6x + 9 y = -9x + 19

Mathematics
1 answer:
Ratling [72]2 years ago
3 0
{(-5,64), (2,1)}

linear equation: y = -9x + 19
quadratic equation: y = x² - 6x + 9

Substitute the y in the quadratic equation by the its value in the linear equation.

-9x + 19 = x² - 6x + 9
      -  19               - 19    *subtract 19 to both sides
-9x         = x² - 6x -10
+9x              + 9x            *add 9x to both sides
0            = x² + 3x - 10
0            = (x + 5) (x - 2) *Factor

Set each factor = 0 and solve
x + 5 = 0    ;      x - 2 = 0
x = -5         ;      x = 2

Find the corresponding value of y using the linear equation.
y = -9x + 19

x = -5                              x = 2
y = -9(-5) + 19               y = -9(2) + 19
y = 45 + 19                    y = -18 + 19
y = 64                            y = 1

(-5,64)                              (2,1)

Check each value on each equation.
y = x² - 6x + 9
(-5,64)                                                  (2,1)
64 = (-5)² - 6(-5) + 9                          1 = 2² - 6(2) + 9
64 = 25 + 30 + 9                                1 = 4 - 12 + 9
64 = 64                                               1 = 1

y = -9x + 19
64 = -9(-5) + 19                                  1 = -9(2) + 19
64 = 45 + 19                                      1 = -18 + 19
64 = 64                                              1 = 1

{(-5,64), (2,1)}

You might be interested in
A baker is filling an order which consists of loaves of bread, bags of rolls, and small boxes of croissants. She includes 8 of e
dlinn [17]

Answer:

Step-by-step explanation:

A

6 0
2 years ago
It have 72 chicken and 4ó3 dogs how many are they in altogether
Alborosie

72 chicken and 4ó3 dogs come to 535 animals altogether.


8 0
3 years ago
Read 2 more answers
The product of x and 9 equals 45
adell [148]

Answer:

5

Step-by-step explanation:

because ?*9=45

45÷9=5

4 0
2 years ago
Read 2 more answers
Question 2: You want to donate 30% of the $400 earned at your yard sale to
lilavasa [31]

Answer:

10%= 40$ 30%=120$

Step-by-step explanation:

ok so u earn 400$ at a yard sale. you divide it by 100 400/100=4. ok so then you multiply four by 10=40 and that is 10% multiply it by 30 u get 120 or 30%

sorry for the bad spelling

4 0
3 years ago
Please help!!! the question is in the picture above— this is geometry
Serga [27]

Use the co‐interior rule, corresponding angle rule, alternate angle rule and vertical opposite angle rule to solve the question above.

angle G5 = angle K1 reason : corresponding angles

angle J1 = angle H3 reason: vertical opposite angles

angle J2 = angle K4 reason: vertical opposite angles

angle G5 = angle K4 reason: co‐ interior angles

angle F6 = angle K4 reason: alternate angle

8 0
2 years ago
Other questions:
  • the ratio of strawberry to banana batter is 2:3 we need 30 cups of batter total what percent of the cake is banana
    12·1 answer
  • Is y = x an additive Relationship? Explain.
    10·1 answer
  • Which is a correct first step for solving this equation? −5(4x−7)+8=3x
    11·2 answers
  • Asquare and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of t
    12·1 answer
  • Solve for x in the triangle, Round your answer to the nearest tenth.
    7·2 answers
  • 30 is 6 multiplied by a number Y as a equation
    5·1 answer
  • Solve the system of equations using substitution.
    6·1 answer
  • Lamar buys $75 worth of clothes. He pays $81, including sales tax. What is the tax rate?
    6·1 answer
  • Altitude vs. speed equations
    5·1 answer
  • The formula C=3.14d can be used to approximate the circumference of a circle given its diameter. Company A manufactures and sell
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!