We can have simultaneous equations with one linear and one quadratic equations. The method for solving these types of equations, differs slightly from the one we use to solve simple simultaneous equations. You start off with two equations, one is quadratic and the other one linear. In this example, both equations are equal to y. Consequently, they must both be equal too. The first step is to write the equation as quadratic = linear. Then you just take all values to one side so that you remain with 0 on the other. Next solve the quadratic equation so that you end up with the possible values of x. Then substitute both values (one after the other) into one of the equations to find both possible values of y. Lastly, you can use the values to create co-ordinates.
Example 1We have solved the simultaneous equation by identifying that both equations are equal to each other. We have then moved all the values to one side of the brackets so that we get a quadratic equation. Next we solved the equation to find the possible values of x which we then substituted into one of the original equations to find the possible values of y. Lastly, we wrote the answers as co-ordinates.
Example 2We have solved that simultaneous equations by merging the two equations (due to the fact that they are both equal to y) and making the new equation a quadratic by moving all the values to one side. Then we solved the quadratic to get the possible values of x and then substituted these values into one of the original equations to find the possible values of y. The last step was to write the answers as co-ordinates.
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