Steps | Solution | ||
1. | Add both the equations, and reduce by common factors. | In this case, we get: 5x + 5y = 25, which has 5 as common term. So, we get: x + y = 5 |
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2. | Subtract one from the other, and reduce by common factors. | In this case, we get: x - y = 1, with no common factor |
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3. | Add and Subtract the two new equations again to get the answer. | In this case, adding them again gives: 2x = 6 or, x = 3 And subtracting, we get: 2y = 4 or, y = 2 Thus, we get: x = 3, y = 2, which is the answer! |
Adding, we get: 68x - 68y = 204 or, x - y = 3 Subtracting, we get: 22x + 22y = 22 or, x + y = 1 Adding again, 2x = 4; or, x = 2 Subtracting again, -2y = 2; or, y = -1 Thus, the solution is: x = 2, y = -1 |
Adding, we get: 2431x - 2431y = -2431 or, x - y = -1 Subtracting, we get: 1479x + 1479y = 7395 or, x + y = 5 Adding again, 2x = 4; or, x = 2 Subtracting again, -2y = -6; or, y = 3 Thus, the solution is: x = 2, y = 3 |
Consider two equations, ax + by = c bx + ay = d Adding, (a + b)x + (b + a)y = c + d or, x + y = (c + d)/(a + b) Subtracting, (a - b)x + (b - a)y = c - d or, (a - b)x - (a - b)y = c - d or, x - y = (c - d)/(a - b) Adding again, we get: (c+d) (c-d) 2x = ----- + ----- (a+b) (a-b) Subtracting again, we get: (c+d) (c-d) 2y = ----- - ----- (a+b) (a-b) Note that, dividing both the equations by 2 provides the solution. |
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