Question

in each diagram below, write the 2 numbers on the size of the eggs that are multiplied together to get the top number of the x but added together to get the bottom number of the x

Answer 1

Explanation

then

$\begin{gathered} x\cdot y=A \\ x+y=B \end{gathered}$

Step 1

replace A and B

$\begin{gathered} x\cdot y=9\rightarrow\text{Equation (1)} \\ x+y=-6\rightarrow Equation(2) \\ \end{gathered}$

solve for x and y,

isolate y in equation 2 and replace in equation (1)

$\begin{gathered} x+y=-6\rightarrow Equation(2) \\ x=-6-y \\ x\cdot y=9\rightarrow\text{Equation (1)} \\ (-6-y)y=9 \\ -6y-y^2-9=0 \\ y^2+6y+9=0 \\ (y+3)^2=0 \\ so,\text{ y=-3} \end{gathered}$

and replace in equation (1) to get x

$\begin{gathered} x\cdot y=9 \\ -3x=9 \\ x=\frac{9}{-3} \\ x=-3 \end{gathered}$

so, for the first X, the number are -3 and -3

Step 2

$\begin{gathered} x\cdot y=4 \\ x+y=4 \\ \end{gathered}$

isolate, x in the second equation and replace in the first one

$\begin{gathered} x+y=4 \\ x=4-y \\ \text{replace} \\ x\cdot y=4 \\ (4-y)y=4 \\ 4y-y^2-4=0 \\ -y^2+4y-4=0 \\ y^2-4y+4=0 \\ (y-2)^2=0 \\ y=2 \end{gathered}$

replace in equation

$\begin{gathered} x+y=4 \\ x+2=4 \\ \text{subtract 2 in both sides} \\ x+2-2=4-2 \\ x=2 \end{gathered}$

Hence, for the second X, the numbers are 2 and 2

using this method you will be abel to solve all the problems in that page

I hope this helps you