the solution to the system of equations is 3x+4y=-6 x-5y=17?

Question

3x+4y= -6
x-5y=17

Answer 1

3x + 4y = -6 --------------------eqn(1)

x - 5y = 17 ---------------------eqn(2)

multiply eqn(2) with 3

3x - 15y = 51 -------------------eqn(3)

subtract eqn(1) from eqn(3)

19y = - 57

y = -57/19 = -3

substitute y value in eqn(1)

3x - 12 = -6

3x = 6

x = 6/3 = 2

so x = 2 and y = -3

Answer 2

this is how we do it :

3x+4y= -6
x-5y=17

x-5y=17 => x = 17 + 5y
plug this x into the other equation : 3x+4y= -6
you will get :
3 * (17 + 5y) + 4y = -6

solve the y
19 y + 3*17 = -6

so
19y = -6 - 3*17
thus y = (-6 - 3*17
)/19

next plug the y into one of the equations that contains an x, and solve the x.

Answer 3

Values of y in two equations:
3x + 4y = - 6
4y = - 6 - 3x
y = (- 6 - 3x)/4

x - 5y = 17
5y = x - 17
y = (x - 17)/5

Value of x (equating values of y):
(- 6 - 3x)/4 = (x - 17)/5
5(- 6 - 3x) = 4(x - 17)
- 30 - 15x = 4x - 68
19x = 38
x = 2

Value of y (substituting x with 2 in the 1st equation):
= (- 6 - 3[2])/4
= (- 6 - 6)/4
= - 12/4
= - 3

Answer: x = 2, y = - 3

Proof (substitute x with 2 and y with - 3 in the 2nd equation):
2 - 5(- 3) = 17
2 + 15 = 17

Answer 4

1) Use the substitution method to solve.
2) First set x and y into an equation.
3) Either plug in y into x-equation or plug in x into the other y-equation.
4) To find the answer for each variable, first solve for x or y. Then you plug in the variable you solved first back into either equation to solve for other variable.

Set up equations.
y=(-6-3x)/4
x=17+5y

Plug x into the y equation.
y=(-6-3[17+5y])/4
y=(-6-51-15y)/4
y=(-57-15y)/4
y=-14.25-3.75y
y+3.75y=-14.25
4.75y=-14.25
y=-3

Plug y into any of the equation.
y=-3, x=17+5y
x=17+5[-3]
x=17-15
x=2

So, answer for x and y is....
x=2, y=-3

Answer 5

3x+4y=-6
x-5y=17

3x+4y=-6
x=17+5y

3(17+5y)+4y=-6
51+15y+4y=-6
51+19y=-6
19y=-57
y=-3
x=17+5(-3)
x=17-15
x=2