Exercise 18 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 angles. Let's start by adding the second equation to the first and solving for the x-variable.

x+y=90 & (I) 2x-y=105 & (II)

SysEqnAdd

(I):Add (II)

x+y+( 2x-y)=90+ 105 2x-y=105

RemovePar

(I): Remove parentheses

x+y+2x-y=90+105 2x-y=105

AddSubTerms

(I):Add and subtract terms

3x=195 2x-y=105

DivEqn

(I):.LHS /3.=.RHS /3.

x=65 2x-y=105

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

x=65 2x-y=105

Substitute

(II):x= 65

x=65 2( 65)-y=105

Multiply

(II):Multiply

x=65 130-y=105

SubEqn

(II):LHS-130=RHS-130

x=65 - y=-25

MultEqn

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

x=65 y=25

We have found that the two angles are 65^(∘) and 25^(∘).