2 by x + 3 by y = 1 and 3x -2y = 0 find x and y
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Answers
Step-by-step explanation:
System of Linear Equations entered :
[1] y=1/3x-3
[2] -2x+y=2
Equations Simplified or Rearranged :
[1] y - x/3 = -3
[2] y - 2x = 2
// To remove fractions, multiply equations by their respective LCD
Multiply equation [1] by 3
// Equations now take the shape:
[1] 3y - x = -9
[2] y - 2x = 2
Graphic Representation of the Equations :
x + 3y = -9 -2x + y = 2
Solve by Substitution :
// Solve equation [2] for the variable y
[2] y = 2x + 2
// Plug this in for variable y in equation [1]
[1] 3•(2x+2) - x = -9
[1] 5x = -15
// Solve equation [1] for the variable x
[1] 5x = - 15
[1] x = - 3
// By now we know this much :
y = 2x+2
x = -3
// Use the x value to solve for y
y = 2(-3)+2 = -4
Solution :
{y,x} = {-4,-3}