College Math

Let us solve a few sets of linear equations to gain a better understanding of the concept. Case I: System of Equatio s with Only One Solution 2 – = 1 ………………….……………………………(1) 3 + 2 = 12 …………………………………………….(2) Solving the first equation for , we get: = 2 – 1 ……………………………………………….(3) Substituting the value of into equation 2, we get: 3 + 2 × (2 − 1) = 12 Solving the equation 3 + 4 – 2 = 12 7 = 14 = 2 Substituting the value of into equation 3, we get: = 2 × 2– 1 = 3 This set of these linear equations has one solution. In other words, these two lines cross at only one point: (2, 3). The graphical representation of this set of linear equations is as follows:

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