Exercise 10 Page 420

We want to find the point of intersection of the two given functions. In a system of equations, the point or points of intersection represent the solutions to the system. Thus, we need to solve the given system of equations. Let's use the Substitution Method to find the solution. To do this, we will 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. For this exercise, y is already isolated in both equations, so we can skip straight to solving! Let's use the expression equal to y in (I) for our initial substitution.
   y=4x-3 & (I) y=9x-13 & (II)

   Substitute

   (II):y= 4x-3

   y=4x-3 4x-3=9x-13

   ▼

   (II): Solve for x

   SubEqn

   (II):LHS-9x=RHS-9x

   y=4x-3 - 5x-3=- 13

   AddEqn

   (II):LHS+3=RHS+3

   y=4x-3 - 5x=- 10

   DivEqn

   (II): .LHS /(- 5).=.RHS /(- 5).

   y=4x-3 x=2
   Great! Now, to find the value of y, we need to substitute x=2 into either one of the equations in the given system. Let's use the first equation.
   y=4x-3 x=2

   Substitute

   (I):x= 2

   y=4( 2)-3 x=5

   ▼

   (I): Evaluate

   Multiply

   (I): Multiply

   y=8-3 x=2

   SubTerm

   (I): Subtract term

   y=5 x=2
   The solution, or point of intersection, to this system of equations is the point (2,5).