Question

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Answer 1

Answer:

$<p style="color:cyan;font-family:cursive;background:black;font size:40px;"> Let’s rearrange the first and third equations in terms of a :</p><p></p><p>⇒a+b=8⇒a=8−b (i) </p><p></p><p>and</p><p></p><p>⇒a+c=13⇒a=13−c(ii) </p><p></p><p>Then, let’s equate (i) and (ii) :</p><p></p><p>⇒8−b=13−c⇒b=c−5(iii) </p><p></p><p>Now, let’s use the second and fourth equations to find expressions for b and c :</p><p></p><p>⇒c−d=6⇒c=6+d(iv) </p><p></p><p>and</p><p></p><p>⇒b+d=8⇒b=8−d(v) </p><p></p><p>Let’s equate (iii) and (v) :</p><p></p><p>⇒c−5=8−d⇒c=13−d(vi) </p><p></p><p>We can now equate (iv) and (vi) :</p><p></p><p>⇒6+d=13−d⇒2d=7∴d=72 </p><p></p><p>Let’s substitute this value of d into (iv) and (v) :</p><p></p><p>∴c=6+(72)=192 </p><p></p><p>and</p><p></p><p>∴b=8−(72)=92 </p><p></p><p>We can use either (i) or (ii) to find a .</p><p></p><p>Let’s try using (i) :</p><p></p><p>∴a=8−(92)=72 </p><p></p><p>Therefore, the solutions to the system of equations is a=72 , b=92 , c=192 , and d=72 .</p><p></p><p> </p>$

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