Question

what is the solution of the system 2x-y=-7 and 4x-y=-4

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the solution of the system of equations, you can solve the system of equations by either substitution or elimination.

Substitution method:
First, solve one of the equations for one variable and substitute it into the other equation.
From the first equation, solve for y:
2x - y = -7
y = 2x + 7

Substitute this expression for y into the second equation:
4x - (2x + 7) = -4
Simplify:
4x - 2x - 7 = -4
Combine like terms:
2x - 7 = -4
Add 7 to both sides:
2x = 3
Divide both sides by 2:
x = 3/2

Now substitute this value of x back into one of the original equations:
2(3/2) - y = -7
3 - y = -7
Subtract 3 from both sides:
-y = -10
Divide both sides by -1 (or multiply by -1 to change the sign):
y = 10

Therefore, the solution to the system of equations is x = 3/2 and y = 10.

Alternatively, you can use the elimination method to solve the system of equations.

Elimination method:
Multiply the first equation by 2 to make the coefficients of y the same in both equations:
2(2x - y) = 2(-7)
4x - 2y = -14

Now rewrite the second equation:
4x - y = -4

Subtract the second equation from the first equation:
(4x - 2y) - (4x - y) = -14 - (-4)
4x - 2y - 4x + y = -14 + 4
-2y + y = -10
Simplify:
-y = -10
Multiply by -1 to change the sign:
y = 10

Now substitute this value of y into either equation to find x:
2x - y = -7
2x - 10 = -7
Add 10 to both sides:
2x = 3
Divide both sides by 2:
x = 3/2

So, the solution to the system of equations is x = 3/2 and y = 10, which matches the result obtained using the substitution method.