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    Solve the simultaneous equations
    2x+y-5=0 and x^2+y^2=0

    Can anyone do it and explain to me how its done?


    So these are your two equations

    2x + y - 5 = 0
    x ^2 + y^2 = 0

    In order to solve this, you need to use the substitution method. This is where you make one equation equal to one variable then substitute it into the other equation. Solve the solutions then substitute them back into any equation to find what the other variable is.

    I'll give you an example, suppose you have these two equations below
    x - 5 = 3y
    2x + y = 4

    Take equation 1 and make x the subject (the second equation usually has powers in it like your question so use the simpler equation). I could make y the subject but it is 3y which means I have to divide the whole equation by 3 which means you have to deal with lots of fractions. If you wanted to make y the subject in my example then choose the second equation.

     x - 5 = 3y \longrightarrow x = 3y + 5

    So now you have one equation equal to the x variable. Let's look at the second equation.
    2x + y = 4 but we know that x = 3y + 5 so substitute this in!

    Therefore: 2x + y = 4 \longrightarrow 2(3y + 5) + y = 4

    Then expand this to get 6y + 10 + y = 4 \longrightarrow 7y = -6

    So y = \frac{-6}{7}

    Now you have y so substitute this into any equation but preferably the simple one so from your example, the first equation is simpler because it doesn't have powers like the second equation does. As you can see in my example, both equations are simple as none of them involve powers so it doesn't matter which one I use.

    So x = 3(\frac{-6}{7})+5 \rightarrow x = \frac{17}{7}

    So x = \frac{17}{7} and y = \frac{-6}{7}

    It is normal to get fractions or integers. If you have a quadratic equation and got two x values then substitute these two x values to get your two y values!

    It doesn't matter whether you work out x or y first, just as long as you get yours solutions is what's important.

    Always double check your answers! So substitute your x and [latex]/y[latex] into any equation. If you're not getting the right answer as you should be then you done something wrong!
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