SOLUTION: solve the following set of equations 2x+3y+z=13 3x+2y+4z=17 4x+5y+2z=24

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

RELATED QUESTIONS
Systems of Equations 1. Solve the following problems for X and Y i these two system... (answered by Alan3354)

2x + 3z = 4 3y + 2z = 5 3x + 4y = −16 (x, y, z) = 2x +... (answered by Alan3354)

Solve. If the system's equations are dependent or it there is no solution, state this. (answered by Alan3354)

Solve. If the system's equations are dependent or it there is no solution, state this. (answered by solver91311)

Expectations As this is a fundamental "hands on" course, it is expected that you master... (answered by ewatrrr)

Systems of Equations 1. Solve the following problems for X and Y in these two system... (answered by solver91311)

1) x+y=9 x+2y=13 x= y= 2) 3x+7y= 24 9x+5y=24 x= y= 3) 4x+y=17 2x+3y+21 x= (answered by Fombitz)

Is it possible to solve the following system of equations through substitution. If it is, (answered by MathLover1)

Solve the following Using Cramer's rule 1.) 8x+5y=7 6x-7y=59 2.) 3x-7y=34 (answered by MathLover1)