write two numbers that multiply to the value on top and add to the value on bottom.

Explanation:

Step1: Let the two numbers be $x$ and $y$.

We have the equations $xy = 7$ and $x + y=8$. From $x + y = 8$, we can express $y = 8 - x$.

Step2: Substitute $y = 8 - x$ into $xy = 7$.

We get $x(8 - x)=7$, which simplifies to $8x - x^{2}=7$, or $x^{2}-8x + 7 = 0$.

Step3: Factor the quadratic equation.

The quadratic equation $x^{2}-8x + 7=0$ can be factored as $(x - 1)(x - 7)=0$.

Step4: Solve for $x$.

Setting each factor equal to zero gives $x - 1=0$ or $x - 7=0$. So $x = 1$ or $x = 7$. When $x = 1$, $y=7$; when $x = 7$, $y = 1$.

Answer:

1, 7