Find the coordinates of the point where lines 3x+5=y and 6y+x=11 intersect

To find the coordinates of the point, we have to solve the equations simultaneously. To do this, we need the same number for the coefficient of x or y in each equation. Arbitrarily, we will chose to match the x coefficients. This means we have to multiply equation 2 by 3 resulting in2) 18y+3x=33We now rearrange for 3x3x=33-18yand substitute into equation 1(33-18y)+5=yWe now solve for y to give y=2We sub this back into equation 2) to give6(2)+x=11therefore x=-1 and the coordinates are (-1,2)