Solve the simultaneous equations: 2x - 3y = 8 and x - 5y = 11

First start by labelling each equation with a letter. 2x - 3y = 8 (A) x - 5y = 11 (B) Next, find a common coefficient to be able to eliminate one of the coefficients. This could be done by multiplying equation B by 2 so that 2x becomes a common coeffiecient between both equations. Ensure to multiply the whole of equation B by 2. 2x - 3y = 8 (A) 2x - 10y = 22 (B) Remove the common coeffienct by subtracting equation A from equation B so that there are no x terms left in the equation. Remember to subtract the equations on both sides of the equals sign. (2x - 3y) - (2x - 10y) = 7y 8 - 22 = -14 7y = -14 Solve to find y by divinding both sides of the equation by 7 y = -2 Substitute the value found for y back into one of the original equations A or B, (here I will demonstrate with equation B) and then solve for x. 2x - 10y = 22 (B) 2x - (10 x -2) = 22 2x - (-20) = 22 2x + 20 = 22 2x = 2 x = 1 Check the answer by substituing the values for x and y into the other original equation, (here I willl be using equation A) 2x - 3y = 8 (A) (2 x 1) - (3 x -2) = 8 2 - (-6) = 8 2 + 6 = 8 If the final equation is correct then you have solved the simultaneous equations! x = 1 y = -2