Solve these equations simultaneously: (1) 5x - 10z = -45 and (2) 9x = -5z + 80
There are two methods to solve this equation. 1) Rearrange equation 2 to get all the xs and zs on the left hand side (9x+5z=80). Multiply either equation to get an equal number of xs or zs in both equations, e.g. multiply equation 2 by 2 to get 18x+10z=160 (this is now equation 3). You can now see you have 10z in both equation 1 and 3, however one is positive and one is negative. An easy way to remember what to do next is the phrase 'same signs subtract', so as you have different signs you do the opposite and add both equations together (if you'd had the same signs you would have subtracted). This cancels out all the zs leaving you with 23x=115. Diving by 23 gives x=5 and you can use this to find out z by substituting it into equation 1 or 2, to give z=7.
- Divide equation 2 by 9 to work out what x equals in terms of z (x=1/9(-5z+80)). You can then substitute this into equation 1 wherever an x appears. This will remove all the xs in this equation, leaving zs which can be rearranged to work out what z is, by collecting all the zs on one side of the equation. Then, as above you can use the calculated z to work out what x is by substituting it in equation 1 or 2.
