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Zolol [24]
3 years ago
9

Solve the system: 2.5(x−3y)−3=−3x+0.5 3(x+6y)+4=9y+19

Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
3 0

Answer:

The value of x and y that satisfy the equations is x = 2 and y = 1

Step-by-step explanation:

Given

2.5(x−3y)−3=−3x+0.5

3(x+6y)+4=9y+19

Required.

Find x and y

We start by opening all brackets

2.5(x−3y)−3=−3x+0.5 becomes

2.5x - 7.5y - 3 = -3x + 0.5

Collect like terms

2.5x + 3x - 7.5y = 3 + 0.5

5.5x - 7.5y = 3.5 ---- Equation 1

In similar vein, 3(x+6y)+4=9y+19 becomes

3x + 18y + 4 = 9y + 19

Collect like terms

3x + 18y - 9y = 19 - 4

3x + 9y = 15

Multiply through by ⅓

⅓ * 3x + ⅓ * 9y = ⅓ * 15

x + 3y = 5

Make x the subject of formula

x = 5 - 3y

Substitute 5 - 3y for x in equation 1

5.5(5 - 3y) - 7.5y = 3.5

27.5 - 16.5y - 7.5y = 3.5

27.5 - 24y = 3.5

Collect like terms

-24y = 3.5 - 27.5

-24y = -24

Divide through by - 24

y = 1

Recall that x = 5 - 3y.

Substitute 1 for y in this equation

x = 5 - 3(1)

x = 5 - 3

x = 2

Hence, x = 2 and y = 1

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Ok im not sure the answer yet so ima work on it at the same time while im explaining it. (The answer will probably be near the end)

We can use the elimination method to eliminate y out. To do that we multiply the first equation by 3.

6x+3y=-12

Now just subtract it from the other equation.

6x+3y=-12
5x+3y=-6

***x=-6***

Usually after doing the elimination method you will have to solve for x but in this case its already solved for you. If you want to find y now you just take the first equation and fill x with -6 and solve for y.

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1. How many real solutions does the quadratic equation x?+9x= -8 have?​
likoan [24]

Answer:

This quadratic equation has 2 solutions.

Step-by-step explanation:

I assume the '?' in your question is meant to be power 2 (²), or else it would not be a quadratic equation. You could write it using the superscript version of 2.

We can solve this equation by expressing it in the form: ax² + bx + c

x² + 9x= -8

x² + 9x + 8 = 0

Now if you know the discriminant, you can simply plug in your values of a, b, and c to see how many solutions there are.

In this case, you would not need the discriminant as there are whole-number factors and hence this can simply be factorised.

x² + 9x + 8 = 0

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For this equation to be true (= 0), x can equal -8 OR -1.

Hence, this quadratic equation has 2 solutions.

5 0
2 years ago
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