solve the system using substitution method -3x+y=2, 8x-15y=7?

Question

explain how you got the answer

Answer 1

y = 3x + 2
Now substitute this in the other equation for the y

8x - 15(3x + 2) = 7

Multiply through teh () by 15

8x - 45x - 30 = 7

Now combine like terms

-37x - 30 = 7

Add 30 to both sides to get the variable alone

-37x = 37
Divide through by -37
x = -1

Plug x value in for x

-3(-1) + y = 2
3 + y = 2
y = -1

Check:

-3(-1) + (-1) = 2 and 8(-1) - 15(-1) = 7
3 -1 = 2 and -8 + 15 = 7
2 = 2 and 7 = 7

So x = -1 and y = -1

Hope this helps

Answer 2

-3x + y = 2 ADD 3x to both sides
y = 2 + 3x
SUBSTITUTE this value for y = (2 + 3x) into the second equaiton; then SOLVE for x

8x -15y = 7
8x - 15(2+3x) = 7
8x - 30 - 45x = 7 ADD 30 to both sides
8x - 45x = 7 +30
-37x = 37 DIVIDE both sides by -37
x = 37/(-37)
x = -1 ANSWER for value of x

SUBSTITUE -1 back into the first equation and SOLVE for y
-3x+y=2
-3(-1) + y = 2
3 + y = 2 SUBTRACT 3 from both sides
y = -1 ANSWER for value of y

CHECK answers in second equation by SUBSTITUTING the values for x and y; x = -1 and y = -1
8x -15y = 7
8(-1) - 15(-1) = 7
-8 + 15 = 7
7 = 7 it checks out

Answer 3

-3x+y=2
8x-15y=7

Since -3x+y=2 then
y = 2 + 3x

Substitute this value into 8x-15y=7
8x - 15(2+3x) = 7
8x - 30 - 45x = 7

-37x = 37
x = -1

Since y =2 + 3x, y = 2 -3 = -1

x = -1, y = -1

CHECK:
-3x + y = -3(-1) + -1 = 3 - 1 = 2
8x - 15y = 8(-1) - 15(-1) = -8 + 15 = 7

Answer 4

y = 2 + 3x
8x - 15(2 + 3x) = 7
8x - 30 - 45x = 7
- 37x = 37
x = - 1

3 + y = 2
y = - 1

x = - 1 , y = - 1