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frozen [14]
2 years ago
5

Solve the following system by elimination 2x-y=9 and 3x+4y=-14

Mathematics
1 answer:
Fofino [41]2 years ago
6 0

2x - y = 9

3x + 4y = -14

To solve this system using elimination, one of the pairs of variable terms must cancel each other out. Their coefficients must be opposites of each other.

Multiply the top equation by 4.

2x - y = 9

4(2x - y = 9)

8x - 4y = 36

Add the equations together.

8x - 4y = 36

3x + 4y = -14

+___________

11x - 0 = 22

11x = 22

x = 2

Substitute 2 for x into either of the original equations to find y.

2x - y = 9

2(2) - y = 9

4 - y = 9

-y = 5

y = -5

Finally, check work by plugging x- and y-values into each original equation.

2(2) - (-5) = 9 --> 4 + 5 = 9 --> 9 = 9 --> True

3(2) + 4(-5) = -14 --> 6 - 20 = -14 --> -14 = -14 --> True

Answer:

x = 2 and y = -5; (2, -5).

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Answer:

The amount of salt required is 0.3685 grams.

Step-by-step explanation:

20.9% of 1 gram of salt is chlorine, which means the grams of chlorine in 1 gram of salt are

\dfrac{20.9\%}{100\%} *1\: gram = 0.209g\: \text{chlorine}

Now, to make 220 ppm solution, it must be that

\dfrac{220}{10^6} = \dfrac{y}{350+y},

where y is the grams of chlorine required.

We rearrange the equation and solve for y:

220(350+y) = 10^6y

77000+220y =10^6y

77000 = (10^6-220)y

y = \dfrac{77000}{999780}

\boxed{y= 0.07702g}

since 1 gram of salt has 0.209 grams of chlorine, 0.07702g of chlorine corresponds to

\dfrac{0.07701}{0.209} = 0.3685g {\text{ of salt. }

Thus the amount of salt required is 0.3685 grams.

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