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kodGreya [7K]
2 years ago
8

Which of these correctly explains the solution of the system of equations shown

Mathematics
1 answer:
borishaifa [10]2 years ago
8 0

The solution of the system of equations is the point (-6, 6), so the correct option is B.

<h3>Which statements are correct about the system of equations?</h3>

Here we have the system of equations:

2x + 3y = 6

x + 3y = 12

First, let's write these two lines in the slope-intercept form:

y = (6 - 2x)/3 = 2 - (2/3)*x

y = (12 - x)/3 = 4 - (1/3)*x

Now, because "y" is the represents the same variable in both equations, we can write:

2 - (2/3)*x = y = 4 - (1/3)*x

Now we can solve that for x.

2 - (2/3)*x =  4 - (1/3)*x

2 - 4 = (2/3)*x - (1/3)*x

-2 = (1/3)*x

3*(-2) = x = -6

Now, to get the y-value of the solution we can evaluate any of the two lines in x = -6, evaluating the first we get:

y =  4 - (1/3)*x = 4 - (1/3)*(-6) = 4 + 2 = 6

Then the solution of the system is the point (-6, 6). Then the correct statement is B:

"The values of x= -6 and y= 6 satisfy both the equations; therefore, (-6, 6) is the solution."

If you want to learn more about systems of equations:

brainly.com/question/13729904

#SPJ1

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Answer:

Step-by-step explanation:

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she will give 1/4 to 20 people

one way to see it is by counting the bars

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6 0
3 years ago
Solve the inequality for x. –2x – 3 &gt; 13 A) x &lt; –5 B) x &lt; –8 C) x &gt; –5 D) x &gt; –8
s344n2d4d5 [400]

Answer:

B x<-8

Step-by-step explanation:

-2x -3> 13

-2x > 13+3

-2x >16

since you will divide both side by a negative number, the operator will change from > to <

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x<-8

5 0
3 years ago
What is cos(45°)?
Andrej [43]

Answer:

\rm \dfrac{\sqrt2}{2}

Step-by-step explanation:

A right angled ∆ is given to us and we need to find out the value of cos 45° ( with rationalized denominator ) . As we know that in a right angle ∆ , the value of cosine is ,

\rm\implies cos\theta =\dfrac{base}{hypotenuse}

In the given triangle ,

  • Value of base = 1
  • Value of hypotenuse = √2

On substituting the respective values ,

\rm\implies cos45^\circ =\dfrac{1}{\sqrt2}

For rationalizing the denominator , multiply numerator and denominator by √2 , we have,

\rm\implies cos45^\circ=\dfrac{1(\sqrt2)}{(\sqrt2)(\sqrt2)}

Simplify ,

\rm\implies \boxed{\pink{\frak{ cos45^\circ=\dfrac{\sqrt2}{2} }}}

6 0
3 years ago
A graph of a linear function is shown on the grid. Which of these best represents 0 of the function? A 8. B 10. C 16. D 24.
harina [27]

answer:

C. 16

explanation:

when x is 0, the y-intercept is 8

coordinates: (0,8) and (4,6)

slope:

\sf \frac{y2-y1}{x2-x1}

\sf \frac{6-8}{4-0}

\sf \frac{-2}{4}

\sf -\frac{1}{2}

equation:

\sf y = mx +b    [ where m is slope and b is y-intercept ]

y = \sf -\frac{1}{2}x +8

solve for x-intercept:

note: zeros of a function are the values of x when f(x) is equal to 0

y = \sf -\frac{1}{2}x +8

0= \sf -\frac{1}{2}x +8

-8= \sf -\frac{1}{2}x

\sf x = -8 * -2

\sf x = 16

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