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
Vinvika [58]
3 years ago
10

Solve the following System of Three Equations: x−3y+z=−15 2x+y−z=−2 x+y+2z=1

Mathematics
1 answer:
SashulF [63]3 years ago
4 0

Answer:

x = -3 , y = 4 , z = 0

Step-by-step explanation:

Solve the following system:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for z:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Solve for z.

Subtract x - 3 y from both sides:

{z = 3 y + (-x - 15)

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Perform a substitution.

Substitute z = -15 - x + 3 y into the second and third equations:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

x + y + 2 (-15 - x + 3 y) = 1

Hint: | Expand the left hand side of the equation x + y + 2 (-15 - x + 3 y) = 1.

x + y + 2 (-15 - x + 3 y) = x + y + (-30 - 2 x + 6 y) = -30 - x + 7 y:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Isolate terms with x to the left hand side.

Subtract 15 - 2 y from both sides:

{z = -15 - x + 3 y

3 x = 2 y - 17

-30 - x + 7 y = 1

Hint: | Solve for x.

Divide both sides by 3:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

-30 - x + 7 y = 1

Hint: | Perform a substitution.

Substitute x = (2 y)/3 - 17/3 into the third equation:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Choose an equation and a variable to solve for.

In the third equation, look to solve for y:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Isolate terms with y to the left hand side.

Add 73/3 to both sides:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 = 76/3

Hint: | Solve for y.

Multiply both sides by 3/19:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

y = 4

Hint: | Perform a back substitution.

Substitute y = 4 into the first and second equations:

{z = -x - 3

x = -3

y = 4

Hint: | Perform a back substitution.

Substitute x = -3 into the first equation:

{z = 0

x = -3

y = 4

Hint: | Sort results.

Collect results in alphabetical order:

Answer:  {x = -3 , y = 4 , z = 0

You might be interested in
−6(x+7)=−4x−2 how many solutions
yaroslaw [1]

Answer: There is one solution, -20

Step-by-step explanation:

-6(x+7)=-4x-2\\\\Distribute\\\\-6x-42=-4x-2\\\\Add(6x)\\\\-42=2x-2\\\\Add(2)\\\\-40=2x\\\\x=-20

There is one solution, -20

Hope it helps <3

8 0
3 years ago
Read 2 more answers
Part B: In complete sentences, explain how a circle can be used to find the circumcenter of the triangle graphed below.
Karo-lina-s [1.5K]

Answer:

Step-by-step explanation:

<u><em>Part B:</em></u>

The center of the circumscribed circle around a triangle is equidistant from vertices of that triangle. To find the circumcenter need to draw at least two perpendicular bisectors to the sides of the given triangle. Point of intersect of them is center of the circumscribed circle.

<u><em>Part C:</em></u>

Coordinates of the midpoint of line BC ( y = - 1 ) are

( \frac{-6+2}{2} , \frac{-1-1}{2} ) = <em>( - 2 , - 1 )</em> and the equation of the line ⊥ to BC is <em>x = - 2</em>

Because BC is ║ to x-axis and m∠A is 90° , the center of the circle is midpoint of BC and r = \frac{BC}{2} = 4

3 0
2 years ago
Find the slope intercept form for the line satisfying the following conditions. Passing through (3,-5) and (5,-9)
Alborosie

Answer:  m = -4 / 2 = -2 / 1 = -2    

Slope (m) = -2

Step-by-step explanation:

5 0
3 years ago
Order the fraction and decimals from least to greatest.<br> 0.78, 0.5, 3/5
ExtremeBDS [4]

Answer:

0.5, 3/5, 0.78

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
I did the first one I need help on this that’s all
Alenkasestr [34]

Answer:

m<A = 70 deg

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180 deg. Add the three measures and set equal to 180. Solve for x. then use the value of x and the expression for m<A to find the measure of angle A.

m<A + m<B + m<C = 180

5x - 25 + 2x + 10 + 3x + 5 = 180

10x - 10 = 180

10x = 190

x = 19

m<A = 5x - 25 = 5(19) - 25 = 95 - 25 = 70

Answer: m<A = 70 deg

6 0
3 years ago
Read 2 more answers
Other questions:
  • a movie theater charges 8$ for all large containers of popcorn Jeffrey graphs the function that gives the total cost y in dollar
    11·1 answer
  • The range of y=x^2 is
    7·1 answer
  • Answer which ever for 13 points!
    8·2 answers
  • Brandy's Auto Wash earns revenues of $6 per customer. In all, how many customers does
    15·1 answer
  • WHAT IS THE AREA OF TRIANGLES?
    8·2 answers
  • 3 equivalent ratio for 21:56
    10·2 answers
  • A bicycle has a listed price of $643.95 before tax. If the sales tax rate is 9.5%, find the total cost of the bicycle with sales
    6·2 answers
  • A circular "Do Not Enter" road sign has a diameter of 54 centimeters. Which measurement is closest to the area of the sign in sq
    11·1 answer
  • Find the solution to the system of equations 2x + y = 3 and x - y = 3.
    10·2 answers
  • Consider the expansion of (x^2+px-3)(3x-5),where p is a constant.If the coefficient of x of the expansion is -44,find the value
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!