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gayaneshka [121]
4 years ago
8

For each of the following system of linear equations, state the number of solutions without solving the system. a) -x+3y=9, -4x+

12y=12 b) 2x-y-4=0,6x=3y+12
Mathematics
1 answer:
MaRussiya [10]4 years ago
7 0

Answer:

<h2>a) ONE SOLUTION</h2><h2>b) INFINITE SYSTEM OF SOLUTIONS</h2>

Step-by-step explanation:

Given the system of equations;

a) x+3y=9

-4x+12y=12

This equation is a linear simultaneous equation with 2 equations and two unknown values. <em>W</em><u><em>hen the number of equations given is equal to the number of unknown variables, this means that the solution sets of the equations are unique and real and will provide us with just one solution.</em></u>

<u><em /></u>

<em>b) </em> For the system of linear equation

2x-y-4=0 .... *3

6x=3y+12  ... *1

First lets multiply equation 1 by 3, om multiplying by 3 we will have;

6x-3y-12 = 0

6x-3y = 0+12

6x-3y = 12

Rearranging equation 2 will give;

6x - 3y = 12

It is seen that both equation ate the same. This means that what we have is one equation with two unknowns. For a system of equation with one equation and two unknowns, there will be infinite number of solutions after solving the equation. <em><u>Hence, the number of solutions for this system of equation is INFINITE </u></em>

<em><u /></em>

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How many solutions exist for the system of equations in the graph?
shutvik [7]

Answer:

Two solutions

Step-by-step explanation:

The number of points of intersections represents the number of solutions to the system of equations. Since the parabola intersects the circle at two points, there are two solutions to the circle.

Furthermore, these two points of intersection are exactly the solutions to the system of equations. Finding the coordinates of the points of intersection will give you the solutions to the system of equations.

8 0
3 years ago
Help me with this question, please!
AURORKA [14]

Answer:

3,432 m²

Step-by-step explanation:

The amount of aluminum in square meters needed to make the mailboxes = 1863(surface area of each mailbox)

Surface area of each mail box = ½(surface area of cylinder) + (Surface area of rectangular prism/box - area of the surface of the box that joins the half-cylinder)

✔️Surface area of ½-cylinder = ½[2πr(h + r)]

r = ½(0.4) = 0.2 m

h = 0.6 m

π = 3.14

Surface area of ½-cylinder = ½[2*3.14*0.2(0.6 + 0.2]

= 0.628(0.8)

Surface area of ½-cylinder = 0.5024 m²

✔️Surface area of the rectangular box/prism = 2(LW + LH + WH)

L = 0.6 m

W = 0.4 m

H = 0.55 m

Surface area = 2(0.6*0.4 + 0.6*0.55 + 0.4*0.55)

Surface area of rectangular box = 1.58 m²

✔️Area of the surface joining the half cylinder and the box = L*W = 0.6*0.4 = 0.24 m²

✅Surface area of 1 mailbox = (0.5024) + (1.58 - 0.24)

= 0.5024 + 1.34

= 1.8424

Amount of aluminum needed to make 1863 mailboxes = 1863 × 1.8424 = 3,432.3912

= 3,432 m²

8 0
3 years ago
What is -4(3-1)+2 simplified
uysha [10]

Answer:

-6

Step-by-step explanation:

Distribute -4(3-1) the answer for that is -12 + 4

-12+4+2 is -6 donald trump rules.

8 0
4 years ago
Read 2 more answers
8 miles is approximately equal to 6 km. How many km are equal to 28 miles? How many miles are equal to 42 km?
Pani-rosa [81]
1 mile = about 1  1/3 km because 8/6  = 1 1/3
so 28 times 1 1/3 = 37 1/3  (first answer)

42 / 6 = 7 
7 miles are in 42 km (2nd answer)
3 0
4 years ago
Of a group of students 5/8 of them are boys. The girls are put into groups so that each group has 1/6 of the total number of stu
Marina86 [1]
I believe the answer is 9.
3 0
3 years ago
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