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
inessss [21]
3 years ago
14

One linear equation is defined by points (1, 6) and (3, 7), while the other is defined by points (3, 6) and (5, 8). Which point

represents the solution of this system of equations
Mathematics
2 answers:
zysi [14]3 years ago
6 0
So we need to find the two lines...y=mx+b where m is the slope and b is the y-intercept.

m=(dy/dx)=(7-6)/(3-1)=1/2 so

y=x/2+b, now I'll use (1,6) to solve for b

6=1/2+b, b=5 1/2=11/2 so

y1=(x+11)/2

now the other line...

m=(8-6)/(5-3)=2/2=1

y2=x+b, using point (3,6) we solve for b

6=3+b, b=3 so

y2=x+3

Since this is just two lines they will only intersect at a single point and when they do, y=y so we can say:

x+3=(x+11)/2

2x+6=x+11

x+6=11

x=5, now use either line to solve for the corresponding y value...

y2=x+3 becomes y=5+3=8 so the solution to this system is the point:

(5,8)
Oksi-84 [34.3K]3 years ago
5 1

Answer:

(5, 8)

Step-by-step explanation:

Since, the linear equation defined by (x_1, y_1) and (x_2, y_2) is,

y-y_1=\frac{x_2-x_1}{y_2-y_1}(x-x_1)

Thus, the linear equation defined by points (1, 6) and (3, 7) is,

y-6=\frac{7-6}{3-1}(x-1)

y-6=\frac{1}{2}(x-1)

2y-12=x-1

\implies x-2y=-11-----(1)

Similarly, the linear equation is defined by points (3, 6) and (5, 8),

y-6=\frac{8-6}{5-3}(x-3)

y-6=\frac{2}{2}(x-3)

y-6=x-3

\implies x-y=-3------(2)

Equation (1) -  equation (2),

-y = -8

⇒ y = 8

From equation (1),

x-2(8)=-11

x-16=-11

x = - 11 + 16 = 5

Hence, point (5,8) represents the solution of this system of equations.

You might be interested in
Find the solution of the system of equations.<br><br> 15x -4y = -50<br><br> 3x - 2y = -16
Fittoniya [83]

Answer:

15x - 4y =-50 -----(i)

3x - 2y=-16 --------(ii)

Using Substitution

From (i)

15x=4y-50

x=4y-50/15

Substitute x=4y-50/[15] into eqn (ii)

3x - 2y= -16

3[4y-50]/15 - 2y =-16

Multiply through by 15 to clear the fraction

3(4y - 50) - 30y=-240

12y - 150 -30y=-240

12y-30y=-240+150

-18y = -90

y=90/18

y=5.

Substitute into any eqn of choice to get x

3x - 2y=-16

3x - 2(5)=-16

3x - 10=-16

3x=-16+10

3x=-6

x=-6/3

x=-2.

x= -2

y=5

5 0
2 years ago
Choose all the expressions that are equal to 5/9 multiply 8
Lesechka [4]

Answer:

4.44

Step-by-step explanation:

the real answer is 4.44444444444

5 0
3 years ago
Can someone help me finish my algebra packet??
MA_775_DIABLO [31]
Happy to help :-)

Please provide us with questions
4 0
3 years ago
What’s the value of <br> tan (3arc cos 3/4)
Volgvan
<h2>Answer: -1.469</h2>

This trigonometric function can be written as:

tan (3 cos^{-1} (\frac{3}{4}))   (1)

Firstly, we have to solve the inner parenthesis:

cos^{-1} (\frac{3}{4})= 41.409   (2)

Substituting (2) in (1):

tan (3(41.409))=tan(124.228)   (4)

Finally we obtain the value:

tan(124.228)=-1.469  

6 0
3 years ago
Read 2 more answers
6 lbs of potatoes cost $72. How many<br> lbs of potatoes can you get with $516?
Rasek [7]

Answer:

42

Step-by-step explanation:

516 divided by 72 = 7.1. You cant use .1 pound . Then you do 6*7 = 42 pounds of potatoes

8 0
3 years ago
Other questions:
  • A bag of marbles contains five red marbles, 12 blue marbles,
    14·1 answer
  • Can someone help me please
    8·1 answer
  • Hillary needs to know if the triangle shown is a right triangle. Which equation should she use to help?
    11·1 answer
  • The sum of 48 and itself, its half and half of the half is added to 18.​
    10·1 answer
  • What is the result of converting 20 ounces into pounds
    7·2 answers
  • Mr. Ramsey orders lunches to be delivered to his workplace for himself and some
    8·2 answers
  • -9h - 15 = 93 Need help. Not that good at solving two step equations. Algebra's tricky. Please solve.
    14·1 answer
  • Slope:<br> what is the slope?
    8·1 answer
  • What is:<br><br>k/3 + 17 = 12?​
    12·2 answers
  • Comprehension Question
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!