All categories

3 years ago

Choose the correct words from the drop-down menu to make a true statement about the system of equations.

Mathematics

1 answer:

lyudmila [28]3 years ago

6 0

Answer:C. It has only one solution

Step-by-step explanation:

The system of equations is expressed as

y = x + 2

Subtracting 2 from the left hand side and the right hand side of the equation, it becomes

x = y - 2 - - - - - - - - - 1

-x + 3y = 6

Multiplying the left hand side and the right hand side of the equation by - 1, it becomes

x - 3y = - 6

Adding 3y to the left hand side and the right hand side of the equation, it becomes

x = 3y - 6 - - - - - - - - 2

Equating equation 1 and equation 2, it becomes

y - 2 = 3y - 6

3y - y = - 2 + 6

2y = 4

y = 4/2 = 2

Substituting y = 2 into equation 1, it becomes

x = 2 - 2 = 0

The solutions are (0, 2)

You might be interested in

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y

lubasha [3.4K]

First find a parameterization for the curve of intersection.

Given the equation of a cylinder, a natural choice for a parameterization would be one utilizing cylindrical coordinates. Here,

$16x^2+y^2=16\implies x^2+\left(\dfrac y4\right)^2=1$

which suggests we could use

$\begin{cases}x(t)=\cos t\\y(t)=4\sin t\\z(t)\end{cases}$

with $0\le t\le2\pi$ , and we get $z(t)$ from the equation of the plane,

$x+y+z=12\implies z(t)=12-x(t)-y(t)=12-\cos t-4\sin t$

Now use the arc length formula:

$\displaystyle\ell=\int_0^{2\pi}\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt$

$\displaystyle\ell=\int_0^{2\pi}\sqrt{\sin^2t+16\cos^2t+(\sin t-4\cos t)^2}\,\mathrm dt$

$\displaystyle\ell=\sqrt2\int_0^{2\pi}\sqrt{\sin^2t-4\cos t\sin t+16\cos^2t}\,\mathrm dt\approx\boxed{24.0878}$

4 0

4 years ago

SOLVE X!!!<br> PLS HELP ASAP

Lady_Fox [76]

Answer:

145°

Step-by-step explanation:

x + 35° = 180° {being linear pair }

x = 180° - 35°

x = 145°

Hope it will help :)

8 0

3 years ago

Read 2 more answers

PLEASE HELP! I WILL MARK BRAINLIEST!!!

oksano4ka [1.4K]

Answer:

-8y+12

Step-by-step explanation:

4(-2y +3)

you can distribute the 4

4 • -2y + 4 • 3

= -8y +12

because they are not like terms, you cannot do anything further.

6 0

3 years ago

Try this please, it's about arcs and angles and I'm just not sure how to do it. Thanks!

Nataly_w [17]

Check the picture below.

the segment LOJ is a diameter, and therefore the arcLCJ made by that diameter will have a central angle of 180°.

that simply means that the arcLC is 180 - 94, or 86°.

the ∡LJC is an inscribed angle that is intercepting the arcLC, and therefore, by the inscribed angle theorem, it'll be half of arcLC.

3 0

4 years ago

Manuel ate 1/3 of the crackers on a plate. His brother ate 1/4 of the crackers. There were 5 crackers left on the plate. How man

rewona [7]

Answer:

12 crackers

Step-by-step explanation:

3 0

3 years ago