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2 years ago

Solve the following system of equations by using the substitution method.

Mathematics

2 answers:

VARVARA [1.3K]2 years ago

8 0

Solution :

Given equations, $x-y=3\\2x+2y=2$

Applying Substitution method to solve the equation.

Solve the first equation $x-y=3$ for x,

$x-y=3\:\Rightarrow x=3+y$

Substitute the value of x in second equation,

$2x+2y=2\\\\\Rightarrow 2(3+y)+2y=2\\\\\Rightarrow 6+2y+2y=2\\\\\Rightarrow6+4y=2\\\\\Rightarrow4y=2-6\\\\\Rightarrow4y=-4\\\\\Rightarrow y=\frac{-4}{4} =-1\\\\\Rigtharrow y=-1$

To calculate the value of x substitute the value of y in first equation

$x-y=3\\\\\Rightarrow x-(-1)=3\\\\\Rightarrow x=3-1=2\\\\\Rightarrow x=2$

Hence, the solution of the equations $x-y=3\\2x+2y=2$ is (2,-1).

gtnhenbr [62]2 years ago

4 0

3,4 would be the answer

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3 years ago

A line segment BK is an angle bisector of ΔABC. A line KM intersects side BC such, that BM = MK. Prove: KM ∥ AB.

weqwewe [10]

Answer:

∠BKM= ∠ABK

Therefore AB ║KM (∵ ∠BKM= ∠ABK and lies between AB and KM and BK is the transversal line)

m∠MBK ≅ m∠BKM (Angles opposite to equal side of ΔBMK are equal)

Step-by-step explanation:

Given: BK is an angle bisector of Δ ABC. and line KM intersect BC such that, BM = MK

TO prove: KM ║AB

Now, As given in figure 1,

In Δ ABC, ∠ABK = ∠KBC (∵ BK is angle bisector)

Now in Δ BMK, ∠MBK = ∠BKM (∵ BM = MK and angles opposite to equal sides of a triangle are equal.)

Now ∵ ∠MBK = ∠BKM

and ∠ABK = ∠KBM

∴ ∠BKM= ∠ABK

Therefore AB ║KM (∵ ∠BKM= ∠ABK and BK is the transversal line)

Hence proved.

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3 years ago

Read 2 more answers

Help me please numbers 7 and 8

Olegator [25]

7. plot the points and then measure the height and base
then find the area of parallelogram 1/2*b*h
8. draw a horizontal line on any point y axis
and then plot r go to 0 and then up one over one repeat the steps and then down one to the right one

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2 years ago

<img src="https://tex.z-dn.net/?f=if%20%5C%3A%20%28%20%5Cfrac%7B3%7D%7B4%7D%20%29%5E%7B6%7D%20%20%5Ctimes%20%28%20%5Cfrac%7B16%7

zhenek [66]

Answer:

Step-by-step explanation:

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{x+2}$

$\frac{3^6}{4^6} \cdot \frac{16^5}{9^5}=\frac{4^{x+2}}{3^{x+2}}$

$\frac{3^6}{4^6} \cdot \frac{(4^2)^5}{(3^2)^5}=\frac{4^{x+2}}{3^{x+2}}$

$\frac{3^6}{4^6} \cdot \frac{4^{10}}{3^{10}}=\frac{4^{x+2}}{3^{x+2}}$

$\frac{3^6}{3^{10}} \cdot \frac{4^{10}}{4^6}=\frac{4^{x+2}}{3^{x+2}}$

$3^{-4} \cdot 4^{4}=4^{x+2}3^{-(x+2)}$

This implies

x+2=4

and

-(x+2)=-4.

x+2=4 implies x=2 since subtract 2 on both sides gives us x=2.

Solving -(x+2)=-4 should give us the same value.

Multiply both sides by -1:

x+2=4

It is the same equation as the other.

You will get x=2 either way.

Let's check:

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{2+2}$

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{4}$

Put both sides into your calculator and see if you get the same thing on both sides:

Left hand side gives 256/81.

Right hand side gives 256/81.

Both side are indeed the same for x=2.

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Musya8 [376]

Step-by-step explanation:

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2. Next we need to figure out how much he spent on the shirts. 5*80=400. So he spent $400 dollars on the shirts.

3. We need to find out the amount of money he made from selling the shirts. 6*93=558

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Answer: Mr. Youngbear made 158 dollars worth of profit after selling 93 T-shirts.

(I dont know if this is correct, but I hope I was able to help!)

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