Question 182618
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Given:
{{{7M+4N=2}}}--------> EQN 1
{{{7M+2N=8}}}--------> EQN 2
Let {{{system(M=highlight(x),N=highlight(y))}}}
Multiply EQN 2 by 2 and subtract from EQN 1:
EQN 2, (7x+2y=8)(2)={{{14x+4y=16}}}
Then,
7x+4y=2, EQN 1
-(14x+4y=16), New EQN 2 * remember to change signs
------------
{{{-7x=-14}}}------>{{{cross(-7)x/cross(-7)=cross(-14)2/cross(-7)}}}
{{{highlight(x=2=M)}}}, subst. in  NEW EQN 2:
{{{14*2+4y=16}}}
{{{4y=16-28=-12}}} -------->{{{cross(4)y/cross(4)=cross(-12)3/cross(4)}}}
{{{highlight(y=-3=N)}}}
It shows, both eqns will meet at point (2,-3):
{{{drawing(300,300,-7,7,-7,7,grid(1),graph(300,300,-7,7,-7,7,(2-7x)/4,(8-7x)/2),circle(2,-3,.18))}}}------>RED>>>> EQN 1; GREEN>>> EQN 2
Thank you,
Jojo</pre>