√(2y) + 3 = 11 √(2y) = 11 - 3 = 8 √2 x √y = 8 √y = 8/√2 y = (8/√2)2 = 64/2 = 32
y = -6
(8 - √32) and (8 + √32), which are approximately 2.343 and 13.657.Let x be one number and y the other. So you have 2 equations with 2 unknowns:(1) x * y = 32(2) x + y = 16Rearranging (2) for y to get y=16-x. Now substitute this expression into equation (1):x * (16 - x) = 3216x - x2 = 32x2 - 16x + 32 = 0Then solve the quadratic formula:x = ( 16 ± √((-16)2 - 4 x 32) ) / 2= ( 16 ± √(256 - 128) ) / 2= ( 16 ± √128) / 2= 8 ± √32If we consider x = 8 + √32:y = 16 - x = 16 - (8 + √32) = 16 - 8 - √32y = 8 - √32and vice-versa.
You plug in the values of x and y and solve 12x + 16y = ? 12(1) + 16(2) = 12 + 32 = 44
2y = 4 (divide both sides by 2 to solve) y = 2
18+y=32 y=14
You add -18... 18 + y = 32 18 + y + (-18) = 32 + (-18) y = 14
√(2y) + 3 = 11 √(2y) = 11 - 3 = 8 √2 x √y = 8 √y = 8/√2 y = (8/√2)2 = 64/2 = 32
It is (32+32)/2 = 32
y = -6
(8 - √32) and (8 + √32), which are approximately 2.343 and 13.657.Let x be one number and y the other. So you have 2 equations with 2 unknowns:(1) x * y = 32(2) x + y = 16Rearranging (2) for y to get y=16-x. Now substitute this expression into equation (1):x * (16 - x) = 3216x - x2 = 32x2 - 16x + 32 = 0Then solve the quadratic formula:x = ( 16 ± √((-16)2 - 4 x 32) ) / 2= ( 16 ± √(256 - 128) ) / 2= ( 16 ± √128) / 2= 8 ± √32If we consider x = 8 + √32:y = 16 - x = 16 - (8 + √32) = 16 - 8 - √32y = 8 - √32and vice-versa.
You plug in the values of x and y and solve 12x + 16y = ? 12(1) + 16(2) = 12 + 32 = 44
2y = 4 (divide both sides by 2 to solve) y = 2
{2+(2x-y)-(3x-y)
29 degrees Let x represent the number of degrees of the smaller angle and y the number of degrees of the larger angle. Because the angles are complementary, x+y=90. From the problem, x=y-32. Now solve the equations by substituting x from the second into the first: y-32+y=90 2y-32=90 2y=90+32=122 y=122/2=61 x=y-32=61-32=29
y-5 = 32 y5 = 1/32 and so y = 1/2
y = 5 - 2x so 4x + 6(5 - 2x) = -2 ie 4x + 30 - 12x = -2 Subtract 30 from each side: 4x - 12x = -32 ie -8x = -32 so x = 4 and y = -3