Firstly, solving simultaneous equations finds the point(s) where two lines on a graph meet. They can either be two linear equations (finding one point of intersection), a linear and a quadratic (can have two points, equations including x² or y²) or a linear and a circle (two points of intersection, equations with x² and y²). There are two methods to solve simultaneous equations: substitution (has to be used for questions including x² and/or y²); elimination (easier for linear equations). As this question involves only linear equations, the elimination method is more suitable. Make the x terms in both equations the same. The easiest way to do this is multiplying the first equation by 2 and the second equation by 3 (when multiplying make sure ALL terms on BOTH sides of the equal sign are multiplied): 6x+4y= 22 6x-15y=60 (It is usually easier to make the x terms the same as most questions will start with the x terms and these will mostly be positive.) The x terms then need to be removed (eliminiated) from the equations (if the y terms were the same then the y terms would need to be eliminated instead). The equations need to be either added to or subtracted from eachother. If the Signs are the Same you Subtract, if the signs are Different you aDD. In this case the x terms are both positive (the same) so subtract the second equation from the first. The y term can then be found: 6x+4y= 22 minus 6x-15y=60 19y=-38 y=-2 Once y has been found it needs to be put back into an equation in order to find x: 3x+(2 X -2) = 11 3x-4=11 3x=15 x=5 The good thing about simultaneous equations is that you can easily check if you have the right answer. Put your x and y value into the other equation (the one not used to find x in this case) and make sure that you get the answer from the question: 2(5)-5(-2) = 10+10 = 20 This shows that the x and y value are correct.

2x^2+21x=-40

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