Exercise 36 Page 28

Since the y-variable is isolated in the first equation, we will use the Substitution Method. To solve a system of linear equations this way, we have to follow 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. As we already know, y is isolated in one equation, so we can skip straight to solving!
   y=1+x & (I) 2x+y=-2 & (II)

   Substitute

   (II): y= 1+x

   y=1+x & (I) 2x+( 1+x)=-2 & (II)

   ▼

   (II):Solve for x

   AddTerms

   (II):Add terms

   y=1+x & (I) 3x+1=-2 & (II)

   SubEqn

   (II):LHS-1=RHS-1

   y=1+x & (I) 3x=-3 & (II)

   DivEqn

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

   y=1+x & (I) x=-1 & (II)
   Great! Now, to find the value of y, we need to substitute x=-1 into either one of the equations in the given system. Let's use the first equation.
   y=1+x & (I) x=-1 & (II)

   Substitute

   (I):x= -1

   y=1+( -1) & (I) x=-1 & (II)

   AddNeg

   (I):a+(- b)=a-b

   y=0 & (I) x=-1 & (II)
   The solution, or point of intersection, to this system of equations is the point (-1,0).