A teacher wrote the equation #3y + 12 = 6x# on the board. For what value of # b# would the additional equation #2y = 4x +b# form a system of linear equations with infinitely many solutions?
Let's review first. When does a system of equations haveinfinitely many solutions? Easy! When they're the same equation. Because when they're the same equation, they will both have identical solutions.
So, we trying to find the value for
are the same equation.
Before we get started, let's organize the equations a little bit so that they're both in
We can see that the
Using simple algebra, we get
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