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3 years ago

Solve the following system of equations for all three variables.

Mathematics

1 answer:

Semenov [28]3 years ago

5 0

Answer:

x=2, z=4, y=-6

Step-by-step explanation:

Add

-9x-y+2z= -4

-6x+y+5z= 2

-9x-6x is -15x

-y+y is 0

2z+5z is 7z

-4+2 is -2

So the equation now looks like this: -15x+7z=-2

Subtract

-6x+y+5z= 2

-4x+y+5z= 6

So the equation will look like this:

-6x+y+5z= 2

-(-4x+y+5z= 6)

-6x+4x is -2x

y-y is 0

5z-5z is 0

2-6 is -4

So the equation now looks like this: -2x=-4

You can find x by dividing -2 on both sides:

x=2

So 2 is x

Now you can substitute x into 2

-15(2)+7z=-2

-30+7z=-2

7z=28

Divide 7 on both sides:

z=4

So now you can substitute z into 4 (For any of the three equation)

-4(2)+y+5(4)=6

-8+y+20=6

20 minus 8 is 12

y+12=6

Subtract 12 on both sides:

y=-6

So the answers are

x=2, z=4, y=-6

Hope this helps!

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2 years ago

Read 2 more answers

A baker buys 19 apples of two different varieties to make pies. The total cost of the apples is $5.10. Granny Smith apples cost

Natasha2012 [34]

The baker bought 7 gala apples, and 12 granny smiths apples

Solution:

Let "x" be the number of gala apples bought

Let "y" be the number of granny smith apples bought

Cost of 1 gala apple = $ 0.30

Cost of 1 granny smith apple = $ 0.25

A baker buys 19 apples of two different varieties to make pies

Therefore,

number of gala apples bought + number of granny smith apples bought = 19

x + y = 19 --------- eqn 1

The total cost of the apples is $5.10

Therefore, we can frame a equation as:

number of gala apples bought x Cost of 1 gala apple + number of granny smith apples bought x Cost of 1 granny smith apple = 5.10

$x \times 0.30 + y \times 0.25 = 5.10$

0.3x + 0.25y = 5.1 -------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 19 - y ---------- eqn 3

Substitute eqn 3 in eqn 2

0.3(19 - y) + 0.25y = 5.1

5.7 - 0.3y + 0.25y = 5.1

5.7 - 0.05y = 5.1

0.05y = 5.7 - 5.1

0.05y = 0.6

y = 12

Substitute y = 12 in eqn 3

x = 19 - 12

x = 7

Thus the baker bought 7 gala apples, and 12 granny smiths apples

6 0

3 years ago

Suppose you invest 16000 at 9% interest and that it is compounded daily. How much will you have in 8 years?

forsale [732]

Answer:

Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one.

Step-by-step explanation:

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4 years ago

I need an accurate answer please

kotykmax [81]

x = –6

Solution:

Given expression is $\sqrt[3]{x-2}+5=3$ .

Step 1: Isolate the radical by subtracting 5 from both sides of the equation.

$\Rightarrow\sqrt[3]{x-2}+5-5=3-5$

$\Rightarrow\sqrt[3]{x-2}=-2$

Step 2: Cube both sides of the equation to remove the cube root.

$\Rightarrow(\sqrt[3]{x-2})^3=(-2)^3$

Cube and cube root get canceled in left side of the equation.

$\Rightarrow\ x-2=-8$

Step 3: To solve for x.

Add 2 on both sides of the equation.

$\Rightarrow\ x-2+2=-8+2$

$\Rightarrow\ x=-6$

Hence the solution is x = –6.

6 0

3 years ago