3x-2y=1 and 2x+y=-4
Multiply second equation by 2.
4x + 2y = -8
3x - 2y = 1
Add the two equations to solve for x. Insert x into one of the equations to solve for y.
I assume you are solving?
from the 2nd:
y = -2x-4
sub into the first
3x - 2(-2x - 4) = 1
3x + 4x + 8 = 1
7x = -7
x = -1
back into y = -2x - 4
y = -2(-1) - 4 = -2
x = -1 , y = -2
Rearange your equations.
3 x - 2 y = 1 Multiply both sides by 2
6 x - 4 y = 2
2x + y = - 4 Multiply both sides by 3
6 x + 3 y = - 12
6 x - 4 y = 2
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6 x + 3 y = - 12
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6 x - 6 x - 4 y - 3 y = 2 - ( - 12 )
0 - 7 y = 2 + 12
- 7 y = 14 Divide both sides by - 7
y = 14 / - 7
y = - 2
Put this value into equation:
3 x - 2 y = 1
3 x - 2 * ( - 2 ) = 1
3 x + 4 = 1 Subtract 4 to both sides
3 x + 4 - 4 = 1 - 4
3 x = - 3 Divide both sides by 3
x = - 3 / 3
x = - 1
The solutions are x = - 1 and y = - 2
To solve this system of equations, you can use the method of substitution or the method of elimination. Let's use the method of elimination:
First, let's multiply the second equation by 2 to make the coefficients of y in both equations the same:
Original equations:
3x - 2y = 1
2x + y = -4
Multiply the second equation by 2:
4x + 2y = -8
Now, add the two equations together:
(3x - 2y) + (4x + 2y) = 1 + (-8)
7x = -7
Divide both sides of the equation by 7:
x = -1
Now, substitute the value of x back into one of the original equations to solve for y. Let's use the second equation:
2(-1) + y = -4
-2 + y = -4
Add 2 to both sides of the equation:
y = -2
Therefore, the solution to the system of equations is x = -1 and y = -2.