SOLUTION: Please help me solve this system: x radical 2 + y radical 3 = 0 3x radical 3 - 5y radical 2 = -38

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Question 1206264: Please help me solve this system:

x radical 2 + y radical 3 = 0
3x radical 3 - 5y radical 2 = -38
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


x%2Asqrt%282%29%2By%2Asqrt%283%29=0
3x%2Asqrt%283%29-5y%2Asqrt%282%29=-38

One standard method for solving a pair of linear equations is elimination. Multiply the first equation by sqrt(3) and the second by sqrt(2) (to make x a multiple of sqrt(6) in both equations):

x%2Asqrt%286%29%2B3y=0
3x%2Asqrt%286%29-10y=-38%2Asqrt%282%29

Multiply the first of these equations by 3 and subtract one equation from the other to eliminate x and solve for y:

3x%2Asqrt%286%29%2B9y=0
3x%2Asqrt%286%29-10y=-38%2Asqrt%282%29
19y=38%2Asqrt%282%29
y=2%2Asqrt%282%29

Substitute that value of y in the original first equation to solve for x:

x%2Asqrt%282%29%2B2%2Asqrt%286%29=0
x%2Asqrt%282%29=-2%2Asqrt%286%29
x=-2%2Asqrt%286%29%2Fsqrt%282%29=-2%2Asqrt%283%29

ANSWER: x=-2%2Asqrt%283%29; y=2%2Asqrt%282%29