Multiply First equation by 2: 6y - 2x = 0Add second equation to this: 6y - 2x + 2x + 2y = 0 + 7Simplify: 8y = 7 so y = 0.875 and x = 2.625
(3, 2)
(-1, 5)
x + 2y = 4 (A) y = 2x + 7 (B) 2*(B) gives: 2y = 4x + 14 Substitute the right hand side for 2y in (A) to give: x + (4x + 14) = 4 Simplify: 5x + 14 = 4 Subtract 14 from both sides: 5x = -10 Divide both sides by 5: x = -2 Substitute for x in (B): y = 2*(-2) + 7 = -4 + 7 = 3 Solution: (x, y) = (-2, 3)
If: 3x+2y = 5x+2y = 7 Then: 3x+2y = 7 and 5x+2y = 7 Subtract the 1st equation from the 2nd equation: 2x = 0 or x = o By substitution: x = 0 and y = 3.5
The slope of the line of 2x plus 2y equals 7 is (7/2x - 1).
If: 3x+2y = 5x+2y = 14 Then: 3x+2y = 14 and 5x+2y =14 Subtract the 1st equation from the 2nd equation: 2x = 0 Therefore by substitution the solutions are: x = 0 and y = 7
x + 2y = 7 2y = -x + 7 y = -(x-7)/2 => -x/2 + 7/2 2x - y = 7 -y = -2x + 7 y = 2x + 7 Since -1/2 is the negative reciporical of 2, the slopes of these equations are perpendicular. Therefore, these two lines are perpendicular.
Multiply First equation by 2: 6y - 2x = 0Add second equation to this: 6y - 2x + 2x + 2y = 0 + 7Simplify: 8y = 7 so y = 0.875 and x = 2.625
7x-2y = 14 -2y = -7x+14 y = 3.5x-7
Sum Numb!
(-1, 5)
(3, 2)
(-1, 5)
x + 2y = 4 (A) y = 2x + 7 (B) 2*(B) gives: 2y = 4x + 14 Substitute the right hand side for 2y in (A) to give: x + (4x + 14) = 4 Simplify: 5x + 14 = 4 Subtract 14 from both sides: 5x = -10 Divide both sides by 5: x = -2 Substitute for x in (B): y = 2*(-2) + 7 = -4 + 7 = 3 Solution: (x, y) = (-2, 3)
2x + 5y = 16 + (-5x) - 2y = 2 That gives 2x + 5y = 2 . . . . . . . . . . (I) and -5x - 2y = - 14 or 5x + 2y = 14 . . . . (II) (I)*5: 10x + 25y = 10 (II)*2: 10x + 4y = 28 Subtracting the second from the first, 21y = -18 so y = -18/21 = -6/7 and then by (I) x = 1 - 5y/2 = 1 - 5/2*(-6/7) = 1 + 15/7 = 22/7 So the ordered pair is (22/7, -6/7)
If -2x +14 = 0, -2x = -14, or x = 7.