Question

Solve the system of equations:
3x+4y+z=7
2y+z=3
-5x+3y+8z=-31

Can't figure out triangular-system method. Help?

Answer 1

x=-58/49
z=-223/49
y=185/49

Those are the solutions. Tell me if you need the steps. (it is going to be a lot)

Answer 2

um, please tell me the basic steps to figure it out, if u dont mind, thanks.

Answer 3

you could prolly upload a pic of your scratch paper with your steps.

Answer 4

3x+4y+z=7
2y+z=3
-5x+3y+8z=-31

Since 2y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2y from both sides.
z=-2y+3

Since the equation was solved for z, replace all occurrences of z in the other equations with the solution (-2y+3).
3x+4y+(-2y+3)=7
z=-2y+3
-5x+3y+8(-2y+3)=-31

Since 4y and -2y are like terms, add -2y to 4y to get 2y.
3x+2y+3=7

Multiply 8 by each term inside the parentheses.
-5x+3y+(-16y+24)=-31

Since 3y and -16y are like terms, add -16y to 3y to get -13y.
-5x-13y+24=-31

Move all terms not containing x to the right-hand side of the equation.
3x=-2y+4

Divide each term in the equation by 3.
x=-(2(y-2))/(3)

Since the equation was solved for x, replace all occurrences of x in the other equations with the solution (-(2(y-2))/(3)).
x=-(2(y-2))/(3)
z=-2y+3
-5(-(2(y-2))/(3))-13y+24=-31

Multiply -2 by each term inside the parentheses.
x=(-2y+4)/(3)

Divide each term in the numerator by the denominator.
x=-(2y)/(3)+(4)/(3)

Multiply -2 by each term inside the parentheses.
-5((-2y+4)/(3))-13y+24=-31

Divide each term in the numerator by the denominator.
-5(-(2y)/(3)+(4)/(3))-13y+24=-31

Combine all similar expressions.
-5((-2y+4)/(3))-13y+24=-31

Multiply -5 by each term inside the parentheses.
-(10(y-2))/(3)-13y+24=-31

Multiply -10 by each term inside the parentheses.
(-10y+20)/(3)-13y+24=-31

Divide each term in the numerator by the denominator.
-(10y)/(3)+(20)/(3)-13y+24=-31

Combine 24+(20)/(3) into a single expression by finding the least common denominator (LCD). The LCD of 24+(20)/(3) is 3.
-(10y)/(3)-13y+(92)/(3)=-31

Combine all similar expressions.
(-10y+92)/(3)-13y=-31

Factor out the GCF of -2 from -10y+92.
(-2(5y-46))/(3)-13y=-31

Move the -1 to the front of the fraction.
-(2(5y-46))/(3)-13y=-31

Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 3.
-(2(5y-46))/(3)-13y*(3)/(3)=-31

Multiply 13y by 3 to get 39y.
-(2(5y-46))/(3)-(39y)/(3)=-31

The numerators of expressions that have equal denominators can be combined. In this case, -(2(5y-46))/(3) and -((39y))/(3) have the same denominator of 3, so the numerators can be combined.
(-2(5y-46)-(39y))/(3)=-31

Combine all similar expressions in the polynomial.
(-49y+92)/(3)=-31

Multiply each term in the equation by 3.
-49y+92=-93

Move all terms not containing y to the right-hand side of the equation.
-49y=-185

Since the equation was solved for y, replace all occurrences of y in the other equations with the solution ((185)/(49)).
y=(185)/(49)

Since the equation was solved for y, replace all occurrences of y in the other equations with the solution ((185)/(49)).
x=-(2((185)/(49)))/(3)+(4)/(3)
z=-2((185)/(49))+3
y=(185)/(49)

Remove the single term factors from the expression.
x=-(370)/(147)+(4)/(3)

Move the minus sign from the numerator to the front of the expression.
x=-(174)/(147)

Combine (4)/(3)-(370)/(147) into a single expression by finding the least common denominator (LCD). The LCD of (4)/(3)-(370)/(147) is 147.
x=-(58)/(49)

Multiply -2 by each term inside the parentheses.
z=-(370)/(49)+3

Combine 3-(370)/(49) into a single expression by finding the least common denominator (LCD). The LCD of 3-(370)/(49) is 49.
z=-(223)/(49)

Since the equation was solved for x, replace all occurrences of x in the other equations with the solution (-(58)/(49)).
x=-58/49
z=-223/49
y=185/49

Hope this helps. :)

Answer 5

thank you so much:)

Answer 6

ǝɯoɔlǝʍ ǝɹ,noʎ :)