Question

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

Answer 1

Answer:

Step-by-step explanation:

-13 and 2

Answer 2

Answer: 2 and -13

Step-by-step 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:

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