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solong [7]
3 years ago
7

X+2y=7 3x-2y=-3 solving systems by substitution

Mathematics
1 answer:
strojnjashka [21]3 years ago
5 0
Move 2y to the right hand side of the equation by subtracting 2y from both sides.
<span>x=−2y+7</span> 
<span>3x−2y=−3

</span>Replace all occurrences of x<span> with the </span>solution<span> found by solving the last </span>equation<span> for </span><span>x.</span><span> In this case, the value substituted is </span><span><span>−2y+7</span>.
</span><span>x=−2y+7</span> 
<span>3(−2y+7)−2y=−3

</span>Simplify each term<span>.
</span><span>x=−2y+7</span> 
<span>−6y+21−2y=−3

</span>Add <span>−6y</span><span> and </span><span>−2y</span><span> to get </span><span><span>−8y</span>.
</span><span>x=−2y+7</span> 
<span>−8y+21=−3

Move 21 to the right hand side of the equation.
</span><span>x=−2y+7</span> 
<span>−8y=−21−3

</span>Subtract 3<span> from </span><span>−21</span><span> to get </span><span><span>−24</span>.
</span><span><span>x=−2y+7</span> 
<span>−8y=−24

</span></span>Divide<span> each </span>term<span> in the </span>equation<span> by </span><span><span>−8</span>.
</span><span>x=−2y+7</span> 
<span>y=3

</span>Replace all occurrences of y<span> with the </span>solution<span> found by solving the last </span>equation<span> for </span><span>y.</span><span> In this case, the value substituted is </span><span>3.
</span><span>x=−2(3)+7</span> 
<span>y=3

</span>Multiply <span>−2</span><span> by </span>3<span> to get </span><span><span>−6</span>.
</span><span>x=−6+7</span> 
<span>y=<span>3

</span></span>Add <span>−6</span><span> and </span>7<span> to get </span><span>1.
</span><span>x=1</span> 
<span>y=3

</span><span>(1,3)</span>
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A farmer raises only ducks and pigs. There are 55 animals in all on his farm, and 146 legs.
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Answer:

Number of ducks = 37

Number of pigs = 18

Step-by-step explanation:

Let,

x be the number of ducks

y be the number of pigs

According to given statement;

x+y=55     Eqn 1

2x+4y=146     Eqn 2 (As ducks will have 2 legs and pigs will have 4)

Multiplying Eqn 1 by 2

2(x+y=55)

2x+2y=110    Eqn 3

Subtracting Eqn 3 from Eqn 2

(2x+4y)-(2x+2y)=146-110

2x+4y-2x-2y=36

2y=36

Dividing both sides by 2

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Putting y=18 in Eqn 1

x+18=55

x = 55-18

x = 37

Hence,

Number of ducks = 37

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