Exercise 20 Page 411

Examining the System of Linear Equations, we see that the y-variables have opposite coefficients. This means that we can use the Elimination Method to solve for the two-digit number. Let's start by adding the second equation to the first and solving for the x-variable.

x+y=12 & (I) x-y=2 & (II)

SysEqnAdd

(I):Add (II)

x+y+( x-y)=12+ 2 x-y=2

RemovePar

(I): Remove parentheses

x+y+x-y=12+2 x-y=2

AddSubTerms

(I):Add and subtract terms

2x=14 x-y=2

DivEqn

(I):.LHS /2.=.RHS /2.

x=7 x-y=2

Now that we have solved for the x-variable, we can substitute this value into the second equation and solve for y.

x=7 x-y=2

Substitute

(II):x= 7

x=7 7-y=2

SubEqn

(II):LHS-7=RHS-7

x=7 - y=-5

MultEqn

(II):LHS * (-1)=RHS* (-1)

x=7 y=5

We have found that the two digit number is 75.