Solve the system by substitution.?

Question

x + 2y = –17
–2x + 3y = –15

Answer 1

x + 2y = –17.....(1)
–2x + 3y = –15.....(2)

Consider (2)
–2x + 3y = –15
-2x = -15 - 3y
-2x = -(3y + 15)
2x = 3y + 15
x = (3y + 15)/2.....(3)

Substitute (3) in (1),
x + 2y = –17
(3y + 15)/2 + 2y = -17
(7y + 15)/2 = -17
7y + 15 = -34
7y = -49
y = -7.....(4)

Substitute (4) in (3)
x = (3y + 15)/2
x = (-21 + 15)/2
x = -6/2
x = -3

x = -3, y = -7 is the solution.

Answer 2

x=-2y-17 now you substitute x in sec0nd equation
(-2) (- 2y - 17) + 3y = -15
4y +34 +3y = -15
7y +34 = -15
7y = - 49
y = - 7
Now you replae y with -7 in first equation and solve for x
x + (2) ( -7) = -17
x = 14 + -17 x = -3 ( -3,-7)

Answer 3

solve the first equation for x
x=-17-2y and substitute x in the second equation:
-2(-17-2y)+3y=-15
34+4y+3y=-15
7y=-49
y=-7
x=-17-2*(-7)
x=-17+14
x=-3

Answer 4

Rewrite the first eq to give x = -17 -2y.

Substitute this wherever x occurs in the second equation and solve for y.

Answer 5

multiply the top equation by 2. add the second equation to the first one. then solve for y. plug what y is into the first (original) equation and solve for x.