Solve the simultaneous equation: 3x-12y=6 , 18y=9x+10y

To solve this question, we must first understand what a simultaneous equation is = an equation where the variables have the same values. So in this example, x and y are the same in both equations. We can use this fact to find what the values of them are.To do this, we must single out one variable in order to substitute it into one of the equations. We can find x in terms of y.We take the first equation:3x-12y=6And manipulate it until we get x by itself on one side.We add -12y to both sides to get:3x=6+12yWe then divide both sides by 3:x=2+4yNow that we have x in terms of y, we can substitute this into the second equation so that we can find the values of the variables:18y=9(2+4y)+10yWe can now manipulate this until we find the value of y.We can minus 10y on both sides:8y=9(2+4y)Now we expand the brackets:8y=18+36yWe can minus 8y from both sides:0=18+28yNow we minus 18 from both sides:-18=28yWe divide both sides by 28:-18/28=yWe can put the y to the left side and simplify to get y:y=-9/14Finally, we can substitute this into one of the equations to find the value of x:3x-12(-9/14)=6We expand brackets:3x+54/7=6We minus 54/7 from both sides:3x=-12/7And finally divide both sides by 3 to find x:x=-4/7