Envision Math 2.0: Grade 8, Volume 2
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Envision Math 2.0: Grade 8, Volume 2 View details
3. Solve Systems by Substitution
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Exercise 16 Page 276

Does either of the equations have an isolated variable in it?

A

Practice makes perfect

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=145-5x & (I) 0.1y+0.5x=14.5 & (II)
y=145-5x & (I) 0.1( 145-5x)+0.5x=14.5 & (II)
y=145-5x & (I) 14.5-0.5x+0.5x=14.5 & (II)
y=145-5x & (I) 14.5=14.5 & (II)

Solving this system of equations resulted in an identity since 14.5 is always equal to itself. Therefore, the lines are the same and have infinitely many intersection points. This result corresponds to option A.