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DiKsa [7]
3 years ago
5

Apr 17, 1:48:02 AM

Mathematics
1 answer:
galben [10]3 years ago
5 0

Answer:

y = 9.54

and, x = 0.08

Step-by-step explanation:

Given that

x - 2y = -19 .......................(1)

3x + 5y = 48 ...............(2)

Based on the above information

Multiply by 3 in equation 1

So,

3x - 6y = -57

3x + 5y = 48

-     -        -

-11y = -105

y = 9.54

So, the x would be

x - 2(9.54) = -19

x - 19.08 = -19

x = -19 + 19.08

x = 0.08

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Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

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Step by step solution :<span>Step  1  :</span> 16 Simplify —— 25 <span>Equation at the end of step  1  :</span><span><span> 16 (x2) - —— = 0 25 </span><span> Step  2  :</span></span>Rewriting the whole as an Equivalent Fraction :

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<span>Common denominator : </span>The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

<span> 2.2 </span>      Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

<span> x2 • 25 - (16) 25x2 - 16 —————————————— = ————————— 25 25 </span>Trying to factor as a Difference of Squares :

<span> 2.3 </span>     Factoring: <span> 25x2 - 16</span> 

Theory : A difference of two perfect squares, <span> A2 - B2  </span>can be factored into <span> (A+B) • (A-B)

</span>Proof :<span>  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 <span>- AB + AB </span>- B2 = 
        <span> A2 - B2</span>

</span>Note : <span> <span>AB = BA </span></span>is the commutative property of multiplication. 

Note : <span> <span>- AB + AB </span></span>equals zero and is therefore eliminated from the expression.

Check :  25  is the square of  5 
Check : 16 is the square of 4
Check : <span> x2  </span>is the square of <span> x1 </span>

Factorization is :       (5x + 4)  •  (5x - 4) 

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Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

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Here's how:

(5x+4)•(5x-4) ————————————— • 25 = 0 • 25 25

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The equation now takes the shape :
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Theory - Roots of a product :

<span> 3.2 </span>   A product of several terms equals zero.<span> 

 </span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span> 

 </span>We shall now solve each term = 0 separately<span> 

 </span>In other words, we are going to solve as many equations as there are terms in the product<span> 

 </span>Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

<span> 3.3 </span>     Solve  :    5x+4 = 0<span> 

 </span>Subtract  4  from both sides of the equation :<span> 
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Divide both sides of the equation by 5:
                     x = -4/5 = -0.800 

Solving a Single Variable Equation :

<span> 3.4 </span>     Solve  :    5x-4 = 0<span> 

 </span>Add  4  to both sides of the equation :<span> 
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Divide both sides of the equation by 5:
                     x = 4/5 = 0.800 

<span><span> x = 4/5 = 0.800
</span><span> x = -4/5 = -0.800
</span></span>
3 0
3 years ago
Read 2 more answers
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