Solve 4x+y=7 and 3x+2y=9
Firstly we identify the problem, in this case we have 2 equations which contain a total of 2 unknowns, it is therefore simultaneous equations.Our first step is to rearrange an equation of our choice to give us a new equation we can substitute in to the other equation. The simplest way in this case is by rearranging the first equation to arrive at y=7-4x. We then look to substitute this into the other equation: 3x+2(7-4x)=9. We then multiply out the brackets, taking care with the signs: 3x+14-8x=9. Collect terms to arrive at -5x+14=9. Rearrange your arrive at 5x=5 therefore x=1. We know look to sub this value into one of the original equations in order to find y. We sub into the first equation as this is the quickest (y has no coefficient) 4+y=7 y=3. It is important to check that x=1 y=3 is the correct solution, we do this by subbing both values into the equations and showing that both equations hold with these values.
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