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
salantis [7]
2 years ago
7

What are the solutions to the following system of equations? x − y = 6 y = x2 −6

Mathematics
1 answer:
anastassius [24]2 years ago
7 0

The solutions to the given system of equations is (0, -6) and (1, -5)  

<h3>Simultaneous equations</h3>

From the question, we are to determine the solutions to the given system of equations

The equations are

x − y = 6 --------- (1)

y = x² −6 ---------- (2)

From equation (1)

x - y = 6

∴ x = 6 + y ------- (3)

Substitute into equation (2)

y = x² −6

y = (6+y)² −6

y = (6+y)(6+y) -6

y = 36 + 6y + 6y +y² -6

y = 36 + 12y + y² - 6

Simplifying

y² + 12y - y + 30 = 0

y² + 11y + 30 = 0

Solve quadratically

y² + 11y + 30 = 0

y² + 6y + 5y + 30 = 0

y(y +6) +5 (y +6) = 0

(y + 5)(y + 6) = 0

y + 5 = 0 OR y + 6 = 0

y = -5 OR y = -6

Substitute the values of y into equation (3)

x = 6 + y

When y = -5

x = 6 + (-5)

x = 6 -5

x = 1

When y = -6

x = 6 + (-6)

x = 6 -6

x = 0

∴ When x = 0, y = -6 and when x = 1, y = -5

Hence, the solutions to the given system of equations is (0, -6) and (1, -5)  

Learn more on Solving simultaneous equations here: brainly.com/question/16863577

#SPJ!

You might be interested in
Which table represents a non-linear function
siniylev [52]
The second table represents a non linear function because the x and y values when graphed do not line up along the line of best fit.
3 0
3 years ago
Calculate sin B in reduced fraction form. Use a slash to separate numerator from denominator, such as 2/3 for "two-thirds."
Deffense [45]
\sin B=\dfrac{24}{25}
4 0
3 years ago
1.29 divided by 1.25 =
Ronch [10]
Answer: 1.032 

1.29/1.25 = 1.032
5 0
3 years ago
Read 2 more answers
Another way to write 4 hundred
MrRa [10]
It could be written like 400 or four hundred.
8 0
3 years ago
Read 2 more answers
What should the balance be in Diane's register?<br><br> Will give BRAINLIEST
MArishka [77]

Answer:

The balance of Dianne's register should be $359.41

Step-by-step explanation:

We can begin at the ending balance on the bank statement at $578.30

Then a check is written for $219.25, so a debit

Next a deposit is made for $140.36, so a credit

Then a withdrawal is made for $140.00, so a debit

This means we can make the equation

578.30-219.25+140.36-140.00=359.41

3 0
3 years ago
Other questions:
  • The coordinates of the vertices of a polygon are shown below. D(–4, 5), E(–1, 5), F(1, 2), and G(–1, –1) What type of polygon is
    13·1 answer
  • Jason took a taxi from his home to the airport. <br> the taxi driver charged an initial fee of $12
    8·1 answer
  • Help me this is due tommorow
    5·2 answers
  • Is 5/6 closest to 0,1/2, and 1
    14·1 answer
  • Im having trouble. can someone please help me with this !
    6·1 answer
  • The area of the parallelogram below is ____ square meters. A parallelogram with height labeled with 8 meters. The top horizontal
    13·2 answers
  • Felipe has a flower bed with area 25/4 ft². He expands the flower bed to have area 75/4 ft². How many square feet of space does
    8·2 answers
  • The characteristics of interest, determining the types of data that are being collected.
    14·1 answer
  • Drag and drop the reasons to correctly complete each box.
    7·1 answer
  • The line y = 2x intersects the line y = x + 6 at the point A. Find the equation of the line that passes through A and has gradie
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!