Question

15x - 12y =13
30x +9y =4
whats the value of x

Answer 1

so assuming that x and y are the same value in both equations we can make the first equation negative (multiply the whole thing by -1) and get

-15x+12y=-13
we multiply it by 2 and get
-30x+24y=-26
we add this to the second equation
(30x+9y=4)+(-30x+24y=-26)
30x-30x+24y+9y=-22
or 33y=-22
divide both sides by 11
3y=-2
divide both sides by 3
y=-2/3

we subtitute it into the first equation
15x-12(-2/3)=13
15x-(-24/3)=13
15x+8=13
subtract 8 from both sides
15x=5
divide both sides by 5
3x=1
divide both sides by 3
x=1/3

so x=1/3
y=-2/3

Answer 2

`\left \{ {15x-12y=13\ \ \atop {30x+9y=4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }} \right. \\\\ \left \{ {{-30x+24y=-26} \atop {30x+9y=4}} \right.\\addition\ method\\\\33y=-22\ \ \ \ | divide\ by\ 33\\\\ y=-(22)/(33)\\\\ 15x=13+12y\\\\ x=(13+12y)/(15)=(13+12*(-(22)/(33)))/(15)=(13-(264)/(33))/(15)=(13-8)/(15)=(1)/(3)\\\\ Solution \ is\ x=(1)/(3).`