Solve the simultaneous equations: 3x +4y = 18, and 5x - 2y = 4

First of all, you would label the equations, so let's call 3x +4y = 18 equation A, and 5x - 2y = 4 equation B. Then you would try to find a way to eliminate one of the variables (either x or y). We can do this by multiplying equation B by 2. Therefore the new equation 2B would equal 10x -4y = 8. We can then eliminate the variable 'y' by adding equation A and 2B together. We would add each individual component, therefore the 'xs' would add together to make (3x+10x) 13x, the 'ys' would add together to make (4x-4x) 0, and the integers would add together to make (18 +8) 26. You would then have the equation 13x = 26 which can then be solved for x (dividing both sides of the equation by 13) to get x = 2. This value for x can then be subbed into either equation A or B in order to find the value of y. Therefore subbing into equation A would give 3(2) + 4y = 18, which rearranging and solving would give a value of y = 3. You can then check your results by subbing both x and y values into the other equation, and seeing if the equation works: 5(2) - 2(3) = 4, which does indeed satisfy the equation. Therefore x = 2 and y = 3