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guapka [62]
3 years ago
11

Solve the system of equations:

Mathematics
1 answer:
Sophie [7]3 years ago
3 0

The solution of the system of equations is (6 , -7)

Step-by-step explanation:

There are two method to solve the system of equations

  • Elimination method: we make the coefficients of one variable in the two equations have same values and different signs, then we add the two equations to eliminate this variable and have an equation of other variable, we solve it to find the other variable, then substitute the value of this variable in one of the two equations to find the first variable
  • Substitution method: We use one of the two equations to find one variable in terms of the other, then substitute it in the second equation to have an equation of the other variable, we solve it to find the other variable, then substitute the value of this variable in the equation of the first variable

Let us use the elimination method with your problem

∵ 3x + 2y = 4 ⇒ (1)

∵ 3x + 6y = -24 ⇒ (2)

- Multiply equation (1) by -1 to eliminate x ⇒ to make the coefficients of x in the two equations have same values and different signs

∵ -3x - 2y = -4 ⇒ (3)

- Add equations (2) and (3)

∴ 4y = -28

- Divide both sides by 4

∴ y = -7

Substitute value of y in equations (1) OR (2) to find x

∵ 3x + 2(-7) = 4

∴ 3x - 14 = 4

- Add 14 for both sides

∴ 3x = 18

- Divide both sides by 3

∴ x = 6

The solution of the system of equations is (6 , -7)

<em>I hope this explanation help you</em>

Learn more:

You can learn more about the system of linear equations in brainly.com/question/6075514

#LearnwithBrainly

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Answer:

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Step-by-step explanation:

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thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

8 0
3 years ago
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