7x-8y=-12 ; -4x+2y=3
7x-8y=-12 ....(*)
4x-2y=-3........(**)
------------------------
Form (**)
-2y=-(3+4x)
Y=(3+4x)/2......(#)
Plug (#) into (*)
7x-8(3+4x)/2=-12
7x-4(3+4x)=-24
7x-12-16x=-24
-9x-12=-24
9x+12=24
3x+4=8
x=4/3
Put x into any of the equation above you would get y
Just spotted typo
Am sorry typing maths with my smartphone isn't easy for me
When you plug (#) into (*)
Go with this
7x-4(3+4x)=-12
7x-12-16x=-12
-9x-12=-12
9x+12=12
3x+4=4
X=0
To solve this system of equations, you can use either the substitution method or the elimination method. Let's use the elimination method to solve these equations.
First, let's multiply the second equation by 2 in order to eliminate the y term:
Original equations:
1) 7x - 8y = -12
2) -4x + 2y = 3
Multiply the second equation by 2:
2) -8x + 4y = 6
Now we can add the two equations together to eliminate the y term:
1) 7x - 8y = -12
+ (-8x + 4y = 6)
Simplifying the equation:
7x - 8y - 8x + 4y = -12 + 6
- x - 4y = -6
Next, let's multiply the equation by -1 to make the x coefficient positive:
-(-x - 4y) = -1 * (-6)
x + 4y = 6
Now we have a simplified equation with the variable x.
Now, we have two equations left:
1) - x - 4y = -6
2) x + 4y = 6
We can now add the two equations together to eliminate the y term:
- x - 4y + x + 4y = -6 + 6
Simplifying the equation:
0 = 0
The result is an equation that is always true, which means these equations are dependent and have infinitely many solutions. This means that any values of x and y that satisfy the original equations will also satisfy the final equation 0 = 0.
Therefore, the system of equations is dependent, and there are infinite solutions.