Exercise 17 Page 276

When solving a system of equations using the Substitution Method, there are three steps.

1. Isolate a variable in one of the equations.
2. Substitute the expression for that variable into the other equation and solve.
3. Substitute this solution into one of the equations and solve for the value of the other variable. For this exercise, y is already isolated in the first equation, so we can skip straight to solving!
   y=3x-10 & (I) 3x+2y=16 & (II)

   Substitute

   (II):y= 3x-10

   y=3x-10 3x+2( 3x-10)=16

   Distr

   (II):Distribute 2

   y=3x-10 3x+6x-20=16

   AddTerms

   (II):Add terms

   y=3x-10 9x-20=16

   AddEqn

   (II): LHS+20=RHS+20

   y=3x-10 9x=36

   DivEqn

   (II): .LHS /9.=.RHS /9.

   y=3x-10 x=4

   Great! Now, to find the value of y, we need to substitute x=4 into the first equation.

   y=3x-10 x=4

   Substitute

   (I):x= 4

   y=3( 4)-10 x=4

   (I): Multiply

   y=12-10 x=4

   SubTerm

   (I): Subtract term

   y=2 x=4

   The solution, or point of intersection, to this system of equations is the point (4,2).