There are many times in physics where you start with two equations and two unknowns. You can always solve for a set of problems if you have the same number of equations as you have unknowns.

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Of of the classic problems that is so common that we learn an equation that has already combined our position & time equation with our acceleration & time equation. The equation we derive assumes that you don’t know the time and one other variable. Our two equations are:

position & time | acceleration & time |
---|---|

Δx = v_{i} ∙ t + ½ a ∙∙ t^{2} | v = a ∙ t + v_{i} |

### TI 83 or TI 4 series calculators

#### Graphing solution

Here are the steps for finding the intersection of two equations. Before you plug in the equations, they both need to be in the *f(x)= *function format. In the following example, the first equation is a momentum conservation equation, and the second is a kinetic energy conservation equation. Both are rearranged so x represents the final velocity of one object, and y represents the final velocity of the other.