Question

simultaneous equation
x-y=-3 and x^2-y=9

Answer 1

Answer on Question # 42728 – Math - Algebra

Simultaneous equation $x-y = -3$ and $x^2-y = 9$.

Solution:

Let's find $x$ and $y$.

$$\left\{ \begin{array}{l} x - y = -3 \\ x^2 - y = 9 \end{array} \right.$$

Let's express $x$ from first expression, and put it in second expression.

$$\left\{ \begin{array}{c} x = y - 3 \\ (y - 3)^2 - y = 9 \end{array} \right.$$

Let's open brackets.

$$\left\{ \begin{array}{c} x = y - 3 \\ y^2 - 6 * y + 9 - y = 9 \end{array} \right.$$

We can get such expression $y^2 - 6 * y + 9 - y = 9$, let's simplify it.

$$y^2 - 7 * y = 0$$ $$y(y - 7) = 0$$

From here: $y = 0$ and $y = 7$.

Now we know $y$, we can find $x \Rightarrow x = -3$ and $x = 4$.

Answer:

Pairs of variables $(-3, 0)$ and $(4, 7)$ will be solution of simultaneous equation.

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