When two lines have infinite solutions, they’re the same line! This means they also share the same equation.

Example:

$$2y+4x=8\6y+hx=24$$

The system of equations above has infinite solutions. What is the value of *h*?

A) 4

B) 6

C) 8

D) 12

**Strategy****:**

**Get both equations into (y=mx+b) form****Set the right sides equal and solve for the constant.**

**Or**

**Notice if one equation can be multiplied up to match the other equation.****Solve for the constant.**

Here is what infinite solutions looks like on a graph: they’re the same line!

Systems of equations with no solutions are parallel lines – they have the same slope and different *y*-intercepts.

If you solve for a system and end up with something like 5 = 3, assuming you did your math correctly, this incorrect equation means *no *solution.

Example:

$$2x=5y-8\3y+1=kx$$

The system of equations above has no solutions. What is the value of *k*?

A) (frac25)

B) (frac65)

C) (frac13)

D) (6)

**Strategy****:**

**Get both equations in (y=mx+b).****Set the slopes equal and solve for the constant.**

Here’s an example of what no solutions looks like on a graph:

The SAT will often use constants with systems of equations. Just remember that they’re only numbers, and you should do the same math you would if they looked like a number.

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