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2 years ago

How many solutions does the system have? y=3x+3 y=-2x+3

Mathematics

2 answers:

STatiana [176]2 years ago

8 0

Answer:

One solution (0, 3).

Step-by-step explanation:

As both expressions in x are equal to y:

3x + 3 = -2x + 3

3x + 2x = 3 - 3

5x = 0

x =0.

So y = 3(0) + 3 = 3.

padilas [110]2 years ago

3 0

Answer:

The system has a unique solution pair (x,y)

Step-by-step explanation:

Since both linear equations are given to you solved for "y", each equation is in "slope-intercept form" which is unique. These equations show that they possess different slopes (signaled in bold in the equations below):

y = 3 x +3

y = -2 x +3

(one has slope "3" and the other one slope "-2"), and therefore they are forced to intersect. One represents a line going up (positive slope) and the other one a line going down (negative slope). That means that the system will intersect in one well defined point on the plane, giving a UNIQUE solution to the system.

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The annual expenditure of the US federal government is approximately 444 trillion dollars.

Alexeev081 [22]

Answer:

4 x 10^8 metres.

[0.0001 x (4 x 10^12)

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3 years ago

Find an equation of the line passing through the pair of points. Write the equation in the form Ax +By = C.

Alexxandr [17]

9514 1404 393

Answer:

5x -y = -37

Step-by-step explanation:

One way to find the coefficients A and B is to use the differences of the x- and y-coordinates:

A = Δy = y2 -y1 = 2 -(-3) = 5

B = -Δx = -(x2 -x1) = -(-7 -(-8)) = -1

Then the constant C can be found using either point.

5x -y = 5(-7) -2 = -37

The equation of the line is ...

5x -y = -37

_____

<em>Additional comment</em>

This approach comes from the fact that the slope of a line is the same everywhere.

$\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\Delta y}{\Delta x}\\\\\Delta x(y-y_1)=\Delta y(x-x_1)\qquad\text{cross multiply}\\\\\Delta y(x-x_1)-\Delta x(y-y_1)=0\qquad\text{subtract y term}\\\\\Delta y(x) -\Delta x(y) = \Delta y(x_1)-\Delta x(y_1)\qquad\text{Ax+By=C form}$

The "standard form" requires that A be positive, so we chose point 1 and point 2 to make sure that was the case.

5 0

2 years ago

There are two numbers whose difference is 1 and the sum of their squares is 61.

goldfiish [28.3K]

The numbers are 6 and 5 because 6-5=1 and 6^2=36 or 6*6=36,5^2=25 or 5*5=25. 36+25=61

4 0

3 years ago

Sarah is making strings of beads in the first string she uses 3 beads and she triples the number of beads in each of the next st

xenn [34]

Answer:

She uses 243 beads for the 5th string.

Step-by-step explanation:

In this problem, we can see a pattern. If she triples the number of beads in each of the next strings, that means that we just take the last number and multiply by 3. If the first string uses 3, then:

The second uses 9, 3 * 3 = 9

The third uses 27, 9 * 3 = 27

The fourth uses 81, 27 * 3 = 81

And the 5th uses 243, 81 * 3 = 243.

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3 years ago

The sum or difference of p and q is the of the x-term in the trinomial.

babymother [125]

Answer:

coefficient..........

4 0

2 years ago