Solve the simultaneous equations: 3x+7y=18 and x+2y=5
- To help us to see what we need to do in this question, I would always line the equations up one above the other, and label them (1) and (2). Here we'll say that (1) is 3x + 7y =18 and (2) is x+ 2y =5 - To solve this problem, we first need to eliminate either the x or the y values so that we can solve for just one of them initially. To do this, we need the same amount of x's in both equations, or the same amount of y's. - This can be done many ways, but one of the simplest ways would be to multiply equation (2) by 3. The important thing to remember is to multiply the whole equation by the same amount, not just the x value. (2) x 3 is 3x + 6y = 15 - Now to remove the x's from our problem to solve for y, we can do (1) - (2). 3x + 7y =28 - 3x + 6y =15 - This gives us a value of y =3 - Now that we have a value for y, we can put this into one of our original equations (it doesn't matter which equation you use). - y =3 into (1) is 3x + 7(3) = 18..... 3x+21=18 - Rearrange the equation to find your value for x. 3x = -3 and so x = -1 - To check your answer, try put your values for x and y into equation (2) and see if it equals the correct number.
