Question

the system of equations 2x+3y-7=0and 6x-5y-11=0​

Answer 1

Step-by-step explanation:

$\sqrt{?} The given system of equations may be written as</p><p>2x+3y−7=0</p><p>6x+5y−11=0</p><p></p><p></p><p>The given system of equations is of the form</p><p>a1x+b1y+c1=0</p><p>a2x+b2y+c2=0</p><p></p><p>where, a1=2,b1=3,c1=−7 and a2=6,b2=5,c2=−11</p><p></p><p>We have, a2a1=62=31 and b2b1=53</p><p></p><p>Clearly, a2a1=b2b1</p><p></p><p>So, the given system of equations has a unique solution.</p><p>To find the solution, we use the cross-multiplication method.</p><p></p><p>By cross-multiplication, we have</p><p>3×−11−5×−7x=2×−11−6×−7−y=2×5−6×31</p><p></p><p></p><p>⇒−33+35x=−22+42−y=10−181</p><p></p><p>⇒2x=−20y=−81</p><p></p><p>⇒x=8−2=−41 and y=−8−20=25</p><p></p><p></p><p>Hence, the given system of equations has a unique solution given by x=−41,y=25.</p><p></p><p>$