Question 167382
1){{{3x+2y=10}}}, EQN 1
{{{2x+y=7}}}, EQN 2
Multiply EQN 2 by {{{-2}}}: --> {{{-4x-2y=-14}}}, then add to EQN 1
{{{-x=-4}}} -->{{{highlight(x=4)}}}--{{{system(3x+2y=10,-4x-2y=-14)}}}
Via EQN 1: {{{3(4)+2y=10}}}
{{{12+2y=10}}} ---> {{{2y=10-12=-2}}} ---> {{{cross(2)y/cross(2)=cross(-2)1/cross(2)1 }}}
{{{highlight(y=-1)}}}
Check Via EQN 2:
{{{2*4+(-1)=7}}}
{{{8-1=7}}}, good
2){{{3x-2y=7}}}, EQN 3
{{{2x-y=8}}} , EQN 4
Multiply EQN 4 by {{{-2}}}---> {{{-4x+2y=-16}}} then add to EQN 3
{{{-x=-9}}} --> {{{highlight(x=9)}}} --{{{system(3x-2y=7,-4x+2y=-16)}}}
Via EQN 3: {{{3*9-2y=7}}}
{{{27-7=2y}}} ---> {{{cross(20)10/cross(2)=cross(2)y/cross(2)}}}
{{{highlight(y=10)}}}
Check Via EQN 4:
{{{4*9-2*10=16}}}
{{{36-20=16}}}, good

3){{{2x+3y=-13}}}, EQN 5
{{{-4x+6y=-10}}}, EQN 6
Multiply EQN 5 by {{{-2}}} ----> {{{-4x-6y=26}}} then add to EQN 6
{{{-8x=16}}} --> {{{x=16/-8=highlight(-2=x)}}} ---{{{system(-4x-6y=26,-4x+6y=-10)}}}
Via EQN 5: {{{(2)(-2)+3y=-13}}}
{{{3y=-13+4=-9}}} ---> {{{cross(3)y/cross(3)=cross(-9)3/cross(3)}}}
{{{highlight(y=-3)}}}
Check Via EQN 6:
{{{(-4)(-2)+(6)(-3)=-10}}}
{{{8+(-18)=-10}}}
{{{-10=-10}}} good
Thank you,
Jojo


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