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What are the solutions to the simultaneous equations of 3x -2y equals 1 and 3x squared -2y squared plus 5 equals 0 showing work 1?
1st equation: 3x-2y = 1 or 3x = 1+2y 2nd equation: 3x^2 -2y^2 +5 = 0 or 3x^2 = 2y^2 -5 Square both sides in 1st equation and multiply all terms in 2nd equation by 3 If: 9x^2 = 1+4y+4y^2 and 9x^2 = 6y^2 -15 Then: 6y^2 -15 = 1+4y+4y^2 => 2y^2 -4y-16 = 0 Dividing all terms by two: y^2 -2y-8 = 0 Factorizing: (y-4)(y+2) = 0 => y = 4 or y = -2 Solutions by substitution: x = 3 and y = 4 or x = -1 and y = -2
How do you write this equation 3x equals 2y plus 3 in function form?
3x = 2y + 3 3x -3 = 2y +3 -3 3x - 3 = 2y (3x -3)/2 = 2y / 2 y = 1/2 x (3x - 3) 3x = 2y +3 3x - 3x = -3x +2y +3 0 = -3x +2y +3 -1 x (0) = -1 x (-3x +2y +3) 0 = 3x - 2y -3
What is the graph of the equation -3x plus 4y equal 12?
-3x + 4y = 12∴ 4y = 3x + 12∴ y = 3x/4 + 3So this is a line with a slope of 3/4, an x-intercept of {0, 3} and a y-intercept of {-4, 0}
Solve -3x plus 4y equals 12?
-3x + 4y = 12 Temporary value of y: 4y = 3x + 12 y = (3x + 12) / 4 Substituting y: -3x + 4 [(3x+12) / 4] = 12 -3x + 12x + 48 = 12 -3x + 12x = 12 - 48 9x = 12 - 48 9x = -36 x = -36 / 9 x = -4 Subtituting x to get the final value of y: -3(-4) + 4y = 12 12 + 4y = 12 4y = 12 - 12 4y = 0 y = 0 Final answer: x = -4 y = 0 Check: -3x + 4y = 12 -3(-4) + 4(0) = 12 12 + 0 = 12 12 = 12 Solution 2: -3x + 4y = 12 Temporay value of x: 3x = 4y - 12 x = (4y - 12) / 3 Substituting x to get the value of y: 3[(4y - 12) / 3] + 4y = 12 12y - 36 + 4y = 12 16y = 12 + 36 16y = 48 y = 48 / 16 y = 3 Substituting y to get the value of x: -3x + 4(3) = 12 -3x + 12 = 12 -3x = 12 - 12 x = 0 Final Answer: x = 0 y = 3 Check: -3(0) + 4(3) = 12 12 = 12
Y intercept of 2y equals -6x plus 8?
2y = -6x + 8 The y intercept occurs when x = 0 2y = 8 therefore y = 4
