Solve the two simultaneous equations: 2x - 5y = 11 and 3x + 2y = 7

Step One: Write the first equation and then write the second equation underneath. Label the first equation A and the second equation B. You can now see clearly that each equation contains an x component and a y component. Step Two: To solve this problem, the x component in equation A needs to be equal to the x component in equation B. Or, the y component in equation A needs to be equal to the y component in equation B. In other words, you need to make either the number in front of the x in both equations the same or the number in front of the y. Step Three: Looking at the x components, you have 2x from equation A and 3x from equation B. In order to make the x equal in both equations, you need to find a common multiple. The quickest way to do that is to simply multiply the 2 and 3. This gives you 2 x 3 = 6. Step Four: Now you know that you want to change both equation A and B so that they each contain 6x. For equation A you need to multiply by 3 (2x x 3 =6x) and for equation B you need to multiply by 2 (3x x 2 = 6x) Step Five: Make sure that you multiply everything in both equations not just the x component. If you multiply the equation A by 3 you should get: 6x – 15y = 33. If you multiply equation B by 2 you should get: 6x + 4y = 14 Step Six: Now that we have made the x components equal we can subtract both equations. Again, write equation A and then equation B underneath. Complete the subtraction in columns starting on the left hand side. 6x – 6x = 0. – 15y – 4y = -19y. 33 – 14 = 19 Simplify -19y=-19 by dividing each side by -19, this gives you y=-1 Step Seven: Now that we know the value of y, all that is left to do is calculate x. We can use our original equation A or B from the start. Substitute y = -1 into equation A: 2x -5(-1) = 11 which gives you: 2x + 5 =11, minus 5 from both sides, 2x=6, then divide both sides by 2, x=3 Your final answer: x=3 and y=-1 Step Eight: Use equation B to check your answers. 3(3) + 2(-1) = 7