Question

Find the integer pair that has the given product and sum. The product is – 26. The sum is – 11.​

Answer 1

Answer: 2 and -13

Explanation:

Assign and set two equations:

• Integer #1 = x
• Integer #2 = y

`\left \{ {{x+y=-11} \atop {x*y=-26}} \right.\\`

Find the value of one variable by rearranging the equation:

`x+y=-11\\\\y=-x-11`

Substitute that y-value into the other equation & solve for x:

`x*y=-26\\\\x*(-x-11)=-26\\\\-x^(2) -11x=-26\\\\x^(2) +11x-26=0\\\\(x+13)(x-2)=0\\\\\left \{ {{x_(1)=-13 } \atop {x_(2) =2}} \right.`

Substitute in the x-values to the rearranged equation to find y:

`y=-x-11\\\\\left \{ {{y=-x_(1) -11=-(-13)-11=13-11=2} \atop {y=-x_(2)-11=-2-11=-13 }} \right.`

Answer 2

Explanation:

-13 and 2