All categories

3 years ago

WHat is the ellimination of x-y=-2 and 7x+2y=-5

1 answer:

3 0

<span>This question is from textbook
</span><span>1. Solve by substitution or elimination method: 3x – 2y = 26 -7x + 3y = -49 Eliminate x: 3x – 2y = 26 -7x + 3y = -49 the coefficients of x are 3 and -7. Ignoring signs temporarily they are 3 and 7. The least common multiple of 3 and 7 is 21. If we multiply the first equation through by 7, there will be a 21x where the 3x is now. If we multiply the second equation by 3, there will be a -21x where the -7x is. And 21x and -21x will cancel out when we add equals to equals. So let's multiply the first equation through by 7 and the second equation through by 3: 7[ 3x – 2y = 26] 3[-7x + 3y = -49] 21x - 14y = 182 -21x + 9y = -147 Draw a line underneath and add equals to equals vertically: 21x - 14y = 182 -21x + 9y = -147 ------------------- 0x - 5y = 35 -5y = 35 Divide both sides by -5 y = -7 Eliminate y: 3x – 2y = 26 -7x + 3y = -49 the coefficients of y are -2 and 3. Ignoring signs temporarily they are 2 and 3. The least common multiple of 2 and 3 is 6. If we multiply the first equation through by 3, there will be a -6y where the -2y is now. If we multiply the second equation by 2, there will be a 6y where the 3y is. And -6y and 6y will cancel out when we add equals to equals. So let's multiply the first equation through by 3 and the second equation through by 2: 3[ 3x – 2y = 26] 2[-7x + 3y = -49] 9x - 6y = 78 -14x + 6y = -98 Draw a line underneath and add equals to equals vertically: 9x - 6y = 78 -14x + 6y = -98 ------------------- -5x + 0y = -20 -5x = -20 Divide both sides by -5 x = 4 So the solution is (x,y) = (4,-7) ==================================== 2. Solve by substitution or elimination method: 4x – 5y = 14 -12x + 15y = -42 Eliminate x: 4x – 5y = 14 -12x + 15y = -42 The coefficients of x are 4 and -12 Ignoring signs temporarily they are 4 and 12. The least common multiple of 4 and 12 is 12. If we multiply the first equation through by 3, there will be a 12x where the 4x is now. We don't need to do anything to the second equation for the 12x and the -12x will cancel out when we add equals to equals. So let's multiply the first equation through by 7 and leave the second equation as it is: 3[ 4x – 5y = 14] -12x + 15y = -42 12x - 15y = 42 -12x + 15y = -42 Draw a line underneath and add equals to equals vertically: 12x - 15y = 42 -12x + 15y = -42 ------------------- 0x + 0y = 0 As you can see, any number may be substituted for x and y and that will always be true, since you'll always get 0 on the left and that will always give 0 and 0 will always equal to 0. So there are infinitely many solutions. This sort of system is called "dependent". We need go no further. We just state that the system is dependent and has INFINITELY MANY solutions. =============================================== 3. Solve by substitution or elimination method: -2x + 6y = 1 10x – 30y = -15 Eliminate x: -2x + 6y = 1 10x – 30y = -15 The coefficients of x are -2 and -10 Ignoring signs temporarily they are 2 and 10. The least common multiple of 2 and 10 is 10. If we multiply the first equation through by 5, there will be a -10x where the -2x is now. We don't need to do anything to the second equation for the 10x and the -10x will cancel out when we add equals to equals. So let's multiply the first equation through by 5 and leave the second equation as it is: 5[ -2x + 6y = 1] 10x - 30y = -15 -10x + 30y = 5 10x - 30y = -15 Draw a line underneath and add equals to equals vertically: -10x + 30y = 5 10x - 30y = -15 ------------------- 0x + 0y = -10 </span>

You might be interested in

By what percent will a fraction decrease if its numerator is increased by 20% and its denominator is increased by 50%?

Angelina_Jolie [31]

Answer:

20%

Step-by-step explanation:

With those changes, the fraction is multiplied by ...

$\dfrac{1+.20}{1+.50}=1-\dfrac{.30}{1.50}=1-0.20$

That is, the value of the fraction is decreased by 20%.

5 0

3 years ago

Read 2 more answers

Q and r are independent events. if p(q) = 1/4 and p(r)=1/5, find p(q and r)

klasskru [66]

Answer:

(b) $\frac{7}{30}$

Step-by-step explanation:

When two p and q events are independent then, by definition:

P (p and q) = P (p) * P (q)

Then, if q and r are independent events then:

P(q and r) = P(q)*P(r) = 1/4*1/5

P(q and r) = 1/20

P(q and r) = 0.05

In the question that is shown in the attached image, we have two separate urns. The amount of white balls that we take in the first urn does not affect the amount of white balls we could get in the second urn. This means that both events are independent.

In the first ballot box there are 9 balls, 3 white and 6 yellow.

Then the probability of obtaining a white ball from the first ballot box is:

$P (W_{u_1}) = \frac{3}{9} = \frac{1}{3}$

In the second ballot box there are 10 balls, 7 white and 3 yellow.

Then the probability of obtaining a white ball from the second ballot box is:

$P (W_{u_2}) = \frac{7}{10}$

We want to know the probability of obtaining a white ball in both urns. This is: P( $W_{u_1}$ and $W_{u_2}$ )

As the events are independent:

P( $W_{u_1}$ and $W_{u_2}$ ) = P ( $W_{u_1}$ ) * P ( $W_{u_2}$ )

P( $W_{u_1}$ and $W_{u_2}$ ) = $\frac{1}{3}* \frac{7}{10}$

P( $W_{u_1}$ and $W_{u_2}$ ) = $\frac{7}{30}$

Finally the correct option is (b) $\frac{7}{30}$

3 0

3 years ago

To buy a car, Ahmed borrowed $15000 for 3 years at an annual simple interest rate of 9%. how much interest will he pay if he pay

allochka39001 [22]

4,050$ and 19,050 that is your answer

3 0

2 years ago

Donovan reaches into a jar containing 6 red marbles, 3 blue marbles, 4 yellow marbles, and 5 green marbles,

vredina [299]

12 out of 18. This is because there is 6 red marbles and 18 of them all together. The question states the probability of the red marble NOT being chosen therefore you need to take away 6 from 18 leaving you with 12. I hope this made sense :)

5 0

3 years ago

Answer using steps: An ice cream shop sells ice cream cones with exactly 1 of 3 ice cream flavors in the cone. The 3 flavors are

xeze [42]

Step-by-step explanation:

udhfhxhsjdjejdbcjdxbshajdddjwjed

4 0

3 years ago