Question 167383
1){{{4y=3x+6}}}------------> EQN 1
{{{2x-3y=-5}}} ------------> EQN 2
On EQN 1,
{{{4y=3x+6}}} ---> {{{cross(4)y/cross(4)=(3x+6)/4}}}
{{{y=(3/4)(x)+(6/4)}}}, reduced ----> {{{y=(3/4)x+(3/2)}}}--> Subst. in EQN 2
{{{2x-3((3/4)x+(3/2))=-5}}}
{{{2x-(9/4)x-(9/2)=-5}}}
{{{(8x-9x)/4=-5+(9/2)}}}, combine similar terms, add/subtract
{{{(-1x/4)=(-10+9)/2}}}
{{{(-1/4)x=(-1/2)}}} --> {{{cross(-1/4)x/cross(-1/4)=(-1/2)/(-1/4)}}}
{{{x=(-1/cross(2)1)(cross(-4)2/1)}}}
{{{highlight(x=2)}}}
Via EQn 1: {{{4y=3(2)+6}}}
{{{cross(4)y/cross(4)=(6+6)/4=12/4=3}}} --> {{{highlight(y=3)}}}
Check via EQN 1:
{{{4(3)=3(2)+6}}}
{{{12=6+6}}}
{{{12=12}}}, good
.
2){{{5x-3y=1}}} ----------> EQN 3
{{{2x-3y=-5}}} -----------> EQN 4
On EQN 3:
{{{5x=3y+1}}} ----> {{{cross(5)x/cross(5)=(3y+1)/5}}}
{{{x=(3/5)y+(1/5)}}} ---> subst. in EQN 4
{{{2((3/5)(y)+(1/5))-3y=-5}}}
{{{(6/5)y+(2/5)-3y=-5}}}, combine similar terms
{{{(2/5)+5=3y-(6y/5)}}}
{{{(2+25)/5=(15y-6y)/5}}}
{{{27/5=9y/5}}}
{{{cross(9/5)y/cross(9/5)=(27/5)/(9/5)}}}
{{{y=(27/cross(5))(cross(5)/9)=highlight(27/9=3=y)}}}
Via EQN 3:
{{{x=(cross(3)1/5)(27/cross(9)3)+(1/5)=(27/15)+(1/5)=(27+3)/15=30/15}}}
{{{highlight(x=2)}}}
check Via EQN 4:
{{{2(2)-3(27/9)=-5}}}
{{{4-cross(3)1(27/cross(9)3)=-5}}}
{{{4-9=-5}}}
{{{-5=-5}}}, good
Thank you,
Jojo