Please check my system of linear equations using any algebraic method. Show the check,if possible.
8x-6y=12 / 12x-9y=18
8x-6y=12 (eq.1)
12x-9y=18 (eq.2)
4x-3y=6 (eq.1)
4x-3y=6 (eq.2)
y=4x-6 / 3
Check:
Thank you for your help.
8x-6y=12 / 12x-9y=18
reduce the equations;
1)4x-3y=6
3)4x-3y=6
They are the same equation, no solution.
They are the same equation, so infinitely many solutions.
steve is correct, I meant no single unique solution.
To check the system of linear equations, we need to substitute the values of x and y from the solution back into each equation.
From the solution you provided, we have y = 4x - 6/3, which simplifies to y = 4x - 2.
Let's substitute this into the original equations and see if both equations are satisfied.
1) For eq.1:
8x - 6y = 12
8x - 6(4x - 2) = 12
8x - 24x + 12 = 12
-16x = 0
x = 0
2) For eq.2:
12x - 9y = 18
12(0) - 9(4(0) - 2) = 18
0 - 9(-2) = 18
18 = 18
Both equations are satisfied when x = 0.
Now let's find the value of y by substituting x = 0 back into the equation y = 4x - 2:
y = 4(0) - 2
y = -2
So, the solution to the system of linear equations is x = 0 and y = -2.
To check the solution, substitute these values back into the original equations:
1) For eq.1:
8(0) - 6(-2) = 12
12 = 12
2) For eq.2:
12(0) - 9(-2) = 18
18 = 18
Both equations are satisfied when x = 0 and y = -2. The solution has been verified.