anonymous
  • anonymous
Given the system of equations, what is the solution? 2x + 3y = 2 3x - 4y = 20
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
solve either by substitution or by multiplying the first by 3/2 and subtracting that from the second to find y and then solve for x, or use a matrix method...
anonymous
  • anonymous
?
anonymous
  • anonymous
I will solve by elimination: multiply the first equation by 3/2 to get: \[3x + \frac{9}{2}y = 3\] comparing this with the second equation which is \[3x - 4y = 20\] we see that the coefficient of x (the number multiplying it) in both these equations is 3. So if we subtract one equation from the other (either will do) we will eliminate x and be left with an equation in y only which we can solve for y: \[3x-4y -(3x + \frac{9}{2}y) = 20-3\] \[-4y - \frac{9}{2}y = 17\] \[-\frac{17}{2}y = 17\] \[y=-2\] Now substitute y=-2 into ANY one of your starting equations (it doesn't matter which one) to find x: \[3x - 4(-2) = 20\] \[3x = 20 - 8\] \[3x=12\] \[x=4\] So x=4, y=-2

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