For two numbers with sum $S$ and product $P$, they can be the roots of a quadratic equation of the form $t^2 - St + P = 0$. What quadratic does that give you here?

Find two integers that add to $7$ and multiply to $10$. Those will be the possible values for $x$ and $y$.

Once you have the two numbers, remember the condition $x > y$ to decide which one is $x$.

In Desmos, enter the equation y = x^2 - 7x + 10. This quadratic has x-intercepts that correspond to the two numbers that satisfy the system.

Click on the points where the graph crosses the x-axis; Desmos will display their x-coordinates. These two x-values are the possible values for $x$ and $y$. Use the condition $x > y$ and choose the larger x-value as $x$.

From the system, you know

• $x + y = 7$
• $xy = 10$

For two numbers with sum $S$ and product $P$, they are the roots of the quadratic

Here, $S = 7$ and $P = 10$, so $x$ and $y$ are the roots of

Now factor the quadratic equation

Look for two integers that add to $7$ and multiply to $10$. Call them $a$ and $b$ for now. Then the equation factors as

so the two possible values for $t$ (and therefore for $x$ and $y$) are $t = a$ and $t = b$. You will decide which one is $x$ in the next step using $x > y$.

The two integers that add to $7$ and multiply to $10$ are $5$ and $2$, so the quadratic factors as

and the solutions are $t = 5$ and $t = 2$.

This means $\{x, y\} = \{5, 2\}$.

Since the problem states $x > y$, $x$ must be the larger of the two numbers.

Therefore, $x = 5$.