All categories

3 years ago

What is the elimination method for this problem 4x-3y=22 2x-y=10

Mathematics

2 answers:

Katyanochek1 [597]3 years ago

6 0

4x-3y=22
2x-y=10
4y-2y-20
-y=2
y=-2
i think that is the answer...

Firdavs [7]3 years ago

5 0

4x - 3y = 22 ⇒ 4x - 3y = 22 ⇒ 4x - 3y = 22
2x - y = 10 ⇒2(2x - y) = 10 ⇒ 4x - 2y = 10
 5y = 32
 5y = 32
 5 5
 y = 6.4
 4x - 3(6.4) = 22
 4x - 19.2 = 22
 + 19.2 + 19.2
 4x = 41.2
 4x = 19.2
4 4
 x = 4.8
 (x, y) = (4.8, 6.4)

You might be interested in

What is the value of f(−3)?

Daniel [21]

Is that the whole question ?

7 0

3 years ago

y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence

sukhopar [10]

Let

$\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots$

Differentiating twice gives

$\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots$

$\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n$

When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

$\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0$

$\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1) a_{n+2} - a_n\bigg) x^n = 0$

Then the coefficients in the power series solution are governed by the recurrence relation,

$\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}$

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

• If n is even, then n = 2k for some integer k ≥ 0. Then

$k=0 \implies n=0 \implies a_0 = a_0$

$k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}$

$k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}$

$k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}$

It should be easy enough to see that

$a_{n=2k} = \dfrac{a_0}{(2k)!}$

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

$k = 0 \implies n=1 \implies a_1 = a_1$

$k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}$

$k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}$

$k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}$

so that

$a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}$

So, the overall series solution is

$\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)$

$\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}$

4 0

3 years ago

On the grid, draw the graph of y = 2x - 3 for values of x from -2 to 4 Q

Pie

Answer:

Plot these points:(-2,-7) (-1,-5) (0,-3) (1,-1) (2,1) (3,3) (4,5)

Step-by-step explanation:

You need to substitute your x values into the x of the equation y=2(3)-3 to find the y value...

3 0

3 years ago

An airplane is traveling at an altitude of 30,000 feet

Murljashka [212]

Answer:

10 minutes

Step-by-step explanation:

First, find how much higher the airplane has to travel:

35,000 - 30,000

= 5,000

To fine how long it will take, divide 5000 by 500

5000/500

= 10

So, it will take 10 minutes to get above 35,000 feet

5 0

3 years ago

What's 2/3 divided by 1/4

svlad2 [7]

Answer:

8/3 or 2 and 2/3

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers