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dusya [7]
3 years ago
5

20 POINTS!!! HELP ME!!!! Use the linear combination method to solve the system of equations. Explain each step of your solution.

3x-8y=7" " " " x+2y=-7
Mathematics
1 answer:
madreJ [45]3 years ago
7 0

The solution of the system of equations is (-3 , -2)

Step-by-step explanation:

Steps for Using Linear Combinations Method)

  • Arrange the equations with like terms in columns
  • Analyze the coefficients of x or y
  • Add the equations and solve for the remaining variable
  • Substitute the value into either equation and solve

∵ 3 x - 8 y = 7 ⇒ (1)

∵ x + 2 y = -7 ⇒ (2)

- Multiply equation (2) by 4 to make the coefficients of y are equal in

 magnitude and different in sign

∴ 4 x + 8 y = -28 ⇒ (3)

Add equations (1) and (3)

∵ 3 x - 8 y = 7 ⇒ (1)

∵ 4 x + 8 y = -28 ⇒ (3)

∴ 7 x = -21

- Divide both sides by 7

∴ x = -3

Substitute the value of x in equation (2) to find y

∵ x + 2 y = -7 ⇒ (2)

∵ x = -3

∴ -3 + 2 y = -7

- Add 3 to both sides

∴ 2 y = -4

- Divide both sides by 2

∴ y = -2

The solution of the system of equations is (-3 , -2)

Learn more:

You can learn more about the system of the linear equations in brainly.com/question/13168205

#LearnwithBrainly

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Can someone answer this question please answer it correctly if it’s corect I will mark you brainliest
Daniel [21]

Answer:

getting the queen is smaller

5/8

Step-by-step explanation:

There are 4 queens in a 52 card deck

P(queen) = 4/52 = 1/13

There are 12 pairs socks, 3 of which are grey

P(grey socks) = 3/12 = 1/4

1/13 <1/4

So getting a queen is smaller

The possible outcomes

8 +0  9+0   10+0  <em> 11+0</em>

8+1    9+1 <em>    10+1    11+1</em>

8+2<em>   9+2     10+2    11+2</em>

<em>8+3   9+3     10+3    11+3</em>

There are 16 outcomes and 10 of them are after 11, (assuming we add the time to the bedtime)

P (bedtime later than 10) = 10/16 = 5/8

3 0
3 years ago
Decrease £43 by 29% what’s the answer
borishaifa [10]

Answer:

30.53

Step-by-step explanation:

First you must find what 29% of 43 is, in order to do this we must multiply 43 by 29%

43*29% or 43*.29 is 12.47

This means that 29% of 43 is equal to 12.47

So decreasing 43 by 29% would be the same as decreasing 43 by 12.47

43-12.47=30.53

5 0
3 years ago
What 2 numbers add to get 2 and multiply to 4
rusak2 [61]
Factor 4
4=1 times 4
2 times 2
they don't add to 2
set up equation
x+y=2
xy=4

first equation, subtract x from both sides
y=2-x
subsitute for y
x(2-x)=4
distribute
2x-x^2=4
add x^2
2x=x^2+4
subtract 2x
0=x^2-2x+4
use quadratic formula which is
if you have ax^2+bx+c=0 then
x=\frac{ -b+/-\sqrt{b^{2}-4ac} }{2a} so

1x^2-2x+4=0
a=1
b=-2
c=4
x=\frac{ -(-2)+/-\sqrt{(-2)^{2}-4(1)(4)} }{2(1)}
x=\frac{ 2+/-\sqrt{4-16} }{2}
x=\frac{ 2+/-\sqrt{-12} }{2}
we have \sqrt{-12} and that doesn't give a real solution
therefor there are no real solutions
but if you want to solve fully
x=\frac{ 2+/-2\sqrt{-3} }{2}
i=\sqrt{-1}
x=\frac{ 2+/-2i\sqrt{3} }{2}
x=1+/-i\sqrt{3}
x=1-i\sqrt{3} or x=1+i\sqrt{3} (those are the 2 numbers)

 





6 0
3 years ago
Let n be equal to 156% of 70. Which of the following proportions is true?
aniked [119]
Well all u have to do is 156%*70= 109.2 so N= 109.2
6 0
3 years ago
Given: \overline{AC} \perp \overline{BD} AC ⊥ BD and \overline{BD} BD bisects \overline{AC}. AC . Prove: \triangle ABD \cong \tr
Fofino [41]

Answer:

The Proof for

△ABD ≅ △CBD is below

Step-by-step explanation:

Given:

\overline{AC} \perp \overline{BD}

\overline{BD} \ bisects\  \overline{AC}

AD = CD      .........BD bisect AC

To Prove:

△ABD ≅ △CBD

Proof:

In  ΔABD  and ΔCBD  

BD ≅ BD              ....……….{Reflexive Property}

∠ADB ≅ ∠CDB    …………..{Measure of each angle is 90°( \overline{AC} \perp \overline{BD} )}

AD ≅ CD              ....……….{ \overline{BD} \ bisects\  \overline{AC} }

ΔABD  ≅ ΔCBD   .......….{By Side-Angle-Side Congruence test}  ...Proved

4 0
3 years ago
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