Solve the simultaneous equations: 3x+2y=4 and 4x+5y=17

To solve this equation we need to make it so the x's or the y's of each equation are equal. To do this we need to multiply one or both equations so we can take or add one of the equations to the other. We are going to equate the y's for this example, to do this we need to find the lowest common multiple of 5 and 2 which is 10. This means we want both the y values to have a 10 in front of them, which means we have to times equation 1(3x+2y=4) by 5 and equation 2(4x+5y=17) by 2. This gives us the new equations of 15x+10y=20(1) and 8x+10y=34(2). We can now take equation 1 away from equation 2 which gives us 7x=-14 which shows x to be -2. We can then plug this x value into either of the original equations to find our y value. If we plug it into the original equation 1 we get 3(-2)+2y=4 which can rearranged to show that 2y=10 and therefore y=5. This gives us the final answer of x=-2 and y=5