Solve the simultaneous equations. Equation one: 4x – 3y = 7. Equation two: 4x + y = -1.

To solve this question you need to find a value of x and y which satisfies both of the equations. Simultaneous equations can be solved by three methods: substitution, elimination, and graphically. We will use this example to understand the elimination method. The elimination method is where you manipulate the equations, so that when they are combined one of the unknowns 'drops out', or is eliminated. This leaves us with one unknown which we can solve the equation for and find its solution. We can then substitue this first unknown into one of the original two equations to find the second unkown.

The most important thing to remember when solving simultaneous equatiuons is that whatever you do to one side of the equation you must do to the other. In this example, one way we can eliminatie an unknown (4x) is by taking equation two away from equation one and then solving, as explained above. LHS: 4x - 3y - (4x + y) = -4y. RHS: 7- (-1) = 8. Full eqn: -4y = 8. 4y = -8. y = -2. Substitue this into eqn two to find x. 4x -2 = -1. 4x = 1. x = 1/4. Answer: x = 1/4, y = -2. Substitute these unknowns into eqn one to check your working.