Please solve this question by using the strategy Elimination Method or Solve By Substitution. This is the math equation: 1/2x+y=15 and -x-1/3y=-6 2nd Question: 5/6x+1/3y=0 and 1…

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asked Jun 9, 2021 77.7k views

1 Answer

Meilo · Answer 1 · 2021-06-15T20:37:54+0000

First pair of equations :

$(1)/(2)x+y=15\ ..(i)\\\\-x-(1)/(3)y=-6\ ..(ii)$

Multiply 2 to equation (i), we get

$x+2y=30\ ..(iii)$

By Elimination Method, Add (i) and (ii) (term with x eliminate), we get

$2y-(1)/(3)y=30-6\\\\\Rightarrow\ (5)/(3)y=24\\\\\Rightarrow\ y=(24*3)/(5)=14.4$

put y= 14.4 in (iii), we get

$x+2(14.4)=30\Rightarrow\ x=30-28.8=1.2$

hence, x=1.2 and y =14.4

Second pair of equations :

$(5)/(6)x+\frac13y=0\ ..(i)\\\\ \frac12x-(2)/(3)y=3\ ..(ii)$

Multiply 2 to equation (i), we get

$(5)/(3)x+(2)/(3)y=0\ ..(iii)$

Elimination Method, Add (i) and (ii) (term with y eliminate) , we get

$\frac53x+\frac12x=3\Rightarrow\ (10+3)/(6)x=3\\\\\Rightarrow\ (13)/(6)x=3\\\\\Rightarrow\ x=(18)/(13)$

put
x=(18)/(13) in (i), we get

$(5)/(6)((18)/(13))+(1)/(3)y=0\\\\\Rightarrow\ (15)/(13)+(1)/(3)y=0\\\\\Rightarrow\ (1)/(3)y=-(15)/(13)\\\\\Rightarrow\ y=-(45)/(13)$

hence,
x=(18)/(13) and
y=(-45)/(13) .