Add x and y then Divide by the postulate, subtract 7, add 13, then divide by 3.
Let's try an example: 2 < 4 divide both sides by -2 and you get: -1 < -2 which is clearly false. Another example: -4 < -2 divide both sides by -2 and you get: 2 < 1 which is again false. Here is a simple proof: Assume x < y Then subtract y from both sides: x - y < 0 Now subtract x from both sides: -y < -x which is the same is -x > -y Summarizing: x < y implies that -x > -y.
Let's denote the two numbers as x and y. We can set up a system of equations: x + y = 18 and x - y = 4. By solving this system simultaneously, we can find that x = 11 and y = 7. Therefore, the two numbers that add up to 18 and subtract to 4 are 11 and 7.
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x = 2y y = x - 2 or x = 2y subtract 2y to both sides x - 2 = y subtract y and add 2 to both sides x - 2y = 0 multiply by -1 to both sides x - y = 2 -x + 2y = 0 x - y = 2 add these two equations together y = 2 substitute 2 for y into the first equation, x = 2y x = 2(2) = 4 Thus the solution of these linear system of equations is the point (4, 2). Check:
(x^2 - y^2)
x - (y + 2)
The transformation from y = f(x) to y = f(x - 4) - 2
Add x and y then Divide by the postulate, subtract 7, add 13, then divide by 3.
X = -Y + 3 add Y to each side Y + X = 3 subtract X from each side Y = -X + 3
x - 2y = 4 Add 2y to both sides: x = 4 + 2y Subtract 4 from both sides: x - 4 = 2y Divide both sides by 2: (x - 4)/2 = y or y = 0.5x - 2
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Generally, in order to shift a function horizontally you must add or subtract to x- add to move it to the left, subtract to move it to the right. For example: y = 5x shifted left by 1 y = 5(x + 1) y2 + x2 = 4 shifted right by 3 y2 + (x - 3)2 = 4
The line y = x will shift up when you add a value to x and shift down when you subtract a value from x.
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(-x) + (-y) = -(x + y) Example: x = 2, y = 3 -2 + -3 = -5