Question

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what is the value of y in the system of equations below
3x+y+2z=-10
x+5y-2z=-12
-2x+3y=-1

Answer 1

To find the value of y in the given system of equations, we can solve the system using the method of elimination or substitution. Here, we'll use the method of elimination:

Step 1: Multiply the third equation by 2 to make the coefficients of x in the first and third equations opposites:
-2x + 3y = -1 (multiply both sides by 2)
-4x + 6y = -2

Step 2: Add the modified third equation to the second equation to eliminate x:
(x + 5y - 2z) + (-4x + 6y) = -12 + (-2)
x - 4x + 5y + 6y - 2z = -12 - 2
-3x + 11y - 2z = -14 (simplified equation)

Step 3: Add the first equation to the modified third equation to eliminate x:
(3x + y + 2z) + (-3x + 11y - 2z) = -10 + (-14)
y + 12y = -10 - 14
13y = -24

Step 4: Solve for y by dividing both sides of the equation by 13:
y = -24/13

The value of y in the given system of equations is -24/13.