Exercise 18 Page 228

To solve a system of linear equations using the Elimination Method, one of the variable terms needs to be eliminated when one equation is added to or subtracted from the other. This means that either the x- or the y-terms must cancel each other out. 2 x+5 y=60 & (I) 2 x-5 y=- 20 & (II) We can see that the y-terms will eliminate each other if we add Equation (I) to Equation (II). Now we can solve for y by substituting the value of x into Equation (I) and simplifying.

2x+5y=60 x=10

Substitute

(I): x= 10

2( 10)+5y=60 x=10

▼

(I):Solve for y

Multiply

(I): Multiply

20+5y=60 x=10

SubEqn

(I): LHS-20=RHS-20

20+5y-20=60-20 x=10

SubTerms

(I): Subtract terms

5y=40 x=10

DivEqn

(I): .LHS /5.=.RHS /5.

5y5= 405 x=10

CancelCommonFac

(I): Cancel out common factors

5x5= 405 x=10

SimpQuot

(I): Simplify quotient

y= 405 x=10

CalcQuot

(I): Calculate quotient

y=8 x=10

The solution, or point of intersection, of the system of equations is (10,8). To check this solution, we will substitute it back into the given system and simplify. If doing so results in true statements for every equation in the system, our solution is correct.

2x+5y=60 2x-5y=- 20

(I), (II): x= 10, y= 8

2( 10)+5( 8)=60 2( 10)-5( 8)=- 20

(I), (II): Multiply

20+40=60 20-40=- 20

(I), (II): Add and subtract terms

60=60 ✓ - 20=- 20 ✓