Question

What two numbers can be multiplied together to equal -108 and add up to 23

Answer 1

The two numbers are -4 and 27.

Step-by-step explanation:

Let,

The two numbers be x and y

According to given statement;

xy = -108     Eqn 1

x+y=23       Eqn 2

From Eqn 2;

x = 23-y

Putting in Eqn 1

$(23-y)y=-108\\23y-y^2=-108\\0=y^2-23y-108\\y^2-23y-108=0$

Factorizing the equation;

$y^2+4y-27y-108=0\\y(y+4)-27(y+4)=0\\(y+4)(y-27)=0$

Either,

y+4=0,        => y=-4

Or,

y-27=0        => y=27

Now,

Putting y=-4 in Eqn 2

$x+(-4)=23\\x-4=23\\x=23+4\\x=27$

Putting y = 27 in Eqn 2

$x+27=23\\x=23-27\\x=-4$

The two numbers are -4 and 27.

Keywords: linear equation, substitution method

Learn more about substitution method at:

• brainly.com/question/11286417
• brainly.com/question/12884373

#LearnwithBrainly