Answer: 2 and -13
Step-by-step explanation:
Assign and set two equations:
- Integer #1 = x
- Integer #2 = y
[tex]\left \{ {{x+y=-11} \atop {x*y=-26}} \right.\\[/tex]
Find the value of one variable by rearranging the equation:
[tex]x+y=-11\\\\y=-x-11[/tex]
Substitute that y-value into the other equation & solve for x:
[tex]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.[/tex]
Substitute in the x-values to the rearranged equation to find y:
[tex]y=-x-11\\\\\left \{ {{y=-x_{1} -11=-(-13)-11=13-11=2} \atop {y=-x_{2}-11=-2-11=-13 }} \right.[/tex]
