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Crazy boy [7]
2 years ago
6

Solve the following system of equations by substation.

Mathematics
1 answer:
Cerrena [4.2K]2 years ago
7 0

Answer:

C. (-1, 3)

Step-by-step explanation:

Label the 2 equations:

5y= 7x +22 -----(1)

x= -6y +17 -----(2)

Substitute (2) into (1):

5y= 7(-6y +17) +22

5y= -42y +119 +22 <em>(</em><em>Expand</em><em> </em><em>bracket</em><em>)</em>

5y= -42y +141 <em>(</em><em>Simplify</em><em>)</em>

42y +5y= 141 <em>(</em><em>+</em><em>42y</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em>)</em>

47y= 141

y= 141 ÷47 <em>(</em><em>÷</em><em>4</em><em>7</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em>)</em>

y= 3

Substitute y= 3 into (2):

x= -6(3) +17

x= -18 +17

x= -1

Thus, the solution is (-1, 3).

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What slope of the line contain (-2,5) and (6,-2)
Temka [501]

Answer:

-\frac{7}{8}

Step-by-step explanation:

I'm assuming you're asking for the slope of the line that passes through the two given points. To find this, use the slope formula: \frac{y_2-y_1}{x_2-x_1}.

Substitute the point coordinates into the formula.

\frac{-2-5}{6-(-2)} \rightarrow\frac{-7}{8}

The slope of the line is -7/8.

8 0
3 years ago
Janes age is 5 years less than 3 times her brothers age. Janes age is 11 minus her brothers age. How old is Jane?
ANEK [815]

You did not specify the brother's age, so I make a expression, <em>b</em> as the variable.

(3<em>b</em> + 5) - 11

Now do that with the brother age instead of the variable.

3 0
3 years ago
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Triangle XYZ is rotated 90° counterclockwise about the origin. On a coordinate plane, triangle X Y Z has points (1, 3), (4, nega
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-4,1

Step-by-step explanation:

3 1
3 years ago
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Yesterday morning, at 6:00 AM, water started leaking from a tank at a constant rate. The tank contained8,496liters of water at 6
GREYUIT [131]

A linear equation can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) the slope is:

a = \frac{y_2 - y_1}{x_2 - x_1}

The answers are:

a) y = (-12 L/min)*t + 9,000 L

b) 6,840 L

a) Here we know that we can model this situation with a linear equation, we know that the leak starts at 6:00 am, then we define t = 0 as 6:00 am

We know that at 6:42 am  (at t = 42 mins) the tank has 8,496 liters.

And at 7:15 am (at t = 75 mins) the tank has 8,100 liters.

Then we have two points of the line:

(42 mins, 8,496 liters)

(75 mins, 8,100 liters)

Then the slope is:

a = \frac{8,100 liters - 8,496 liters }{75 mins -42 mins } = -12 L/min

So the line will be something like:

y = (-12 L/min)*t + b

To find the value of b, which is the initial volume of water in the tank, we use the point (75 mins, 8,100 liters)

This means that if t = 75 mins, then we have y = 8,100 L

So we can replace these two on the above equation:

8,100 L = (-12 L/min)*75 mins + b

8,100L = -900L + b

8,100L + 900L = b = 9,000 L

Then the linear equation is:

y = (-12 L/min)*t + 9,000 L

b) Now we want to know how much water is in the tank at 9:00 am.

Notice that 9:00 am is 3 hours after 6:00 am, our t = 0.

Then  9:00am is equivalent to t = 180 mins.

So to know the volume of water that there is in the tank at 9:00 am, we just need to evaluate the linear function at t = 180 mins.

y = (-12 L/min)*180 mins + 9,000 L = 6,840 L

If you want to learn more, you can read:

brainly.com/question/24594539

7 0
2 years ago
ben wants to build a fence he has 22 yards of material his garden is 6 3\4 by 4 2\3 does he have enough material
DiKsa [7]
Sent you a pic of the solution to your problem.

7 0
3 years ago
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