Solve the simultaneous equations, 2x-3y=14 and 3x+4y=4

When asked to solve we have to find the value of x and the value of y, as they are simultaneous equations we know the value of y in equation 1 and equation 2 are the same and this is also the same for when we consider the x values. We cannot solve for two unknowns at the same time so we must choose whether to solve for y or for x. In this case, we will solve for y (it doesn't matter which you choose.) To solve for y, we must be able to cancel out the x terms so only y remains and to do this we first must make the x terms the same in both equations. Therefore, we take the lowest common multiple of the numbers attached to the x in both equations, which in this case is 6 and multiply each equation so that the x terms become 6x. To do this we take, 2x-3y=14 (equation 1,) multiply the whole of equation one by 3 this will then become 6x-9y=42 (we can call this equation 3)3x+4y=4 (equation 2,) multiply the whole of equation two by 2 this will then become 6x+8y=8 (we can call this equation 4.) We now need to cancel out the x terms, we do this by either adding equation 3 and equation 4 or subtracting equation 4 from equation 3. To know which to do we must look at whether the x terms are both positive or both negative or one of each, since they are both positive we use the same sign subtract rule. Thus, it is equation 3 - equation 4 where we minus like terms. This will cancel out x as x=0 and we are left with -17y=34. We now want to get y by itself so we do the opposite of what has been done on the y side of the equals, since -17 is attached to the y by multiplication we divide both sides of the equals by -17 so we now know y=-2. As we know the y value we can now solve for x, to do this we substitute the y value into either equation one or equation two (it doesn't matter which you choose.) Substituting the value of y into equation 2, we have 3x+ (4x -2)=4 which simplified is 3x-8=4. Next we want x by itself so we do the opposite of what is on the x side of the equals therefore, we add 8 so we have 3x=12 and then we divide by 3 so x=4. We have now solved the equation and know x=4 and y=-2.