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Question 553450: solve the following set of equations
2x+3y+z=13
3x+2y+4z=17
4x+5y+2z=24
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equations are:
2x+3y+z=13 (equation 1)
3x+2y+4z=17 (equation 2)
4x+5y+2z=24 (equation 3)
multiply equation 1 by -4 and add it to equation 2 to get:
-8x - 12y -4z = -52 plus:
3x + 2y + 4z = 17 equals:
-5x -10y = -35 (equation 4)
multiply equation 1 by -2 and add it to equation 3 to get:
-4x - 6y - 2z = -26 plus:
4x + 5y + 2z = 24 equals:
-y = -2
multiply both sides of this equation by -1 to get:
y = -2
that's one of the values you are looking for.
substitute for y in equation 4 to get:
-5x - 10(2) = -35
simplify to get:
-5x - 20 = -35
add 20 to both sides of the equation to get:
-5x = -15
divide both sides of the equation by -5 to get:
x = 3
that's the second of the values you are looking for.
so far you have:
x = 3
y = 2
substitute for x and y in equation 1 to get:
2(3) + 3(2) + z = 13
simplify to get:
6 + 6 + z = 13
combine like terms to get:
12 + z = 13
substract 12 from both sides of the equation to get:
z = 1
that's the last of the values you are looking for.
you have:
x = 3
y = 2
z = 1
substitute in all 3 original equations to confirm these solutions apply to all of the equations in the system.
your original equations are:
2x+3y+z=13
3x+2y+4z=17
4x+5y+2z=24
after substitution, these equations become:
2(3) + 3(2) + 1 = 13
3(3) + 2(2) + 4(1) = 17
4(3) + 5(2) + 2(1) = 24
after simplification, these equations become:
6 + 6 + 1 = 13
9 + 4 + 4 = 17
12 + 10 + 2 = 24
after combining like terms, these equations becomes:
13 = 13
17 = 17
24 = 24
all equations are true confirming the values for x and y and z are good.
answer is:
x = 3
y = 2
z = 1
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