solving system of equations by substitution

Question

2b=6a-14

3a-b=7

Answer 1

Kenji, there are a few first steps we can take.  What we want to do is "solve" one of the equations for a or b, then substitute the "value" in the other equation for the variable you solved for.

 

Confusing? Let's clear it up.

 

Let's solve for b in the first equation.  We simply divide both sides by 2 and get b = 3a - 7.

 

Now, we can take the 3a - 7 and substitute it for b in the 2nd equation.  We rewrite the equation to say 3a - (3a - 7) = 7.

 

Distributing, we get 3a - 3a + 7 = 7. Combining like terms, we get 7 = 7.

 

If we end up with the same thing on both sides of the equal sign, this means we have infinite solutions.  In other words, if we graph both equations, they are the same line.

 

Hope this helps!