To solve the simultaneous equation 1.4x + 3y = -1 2y - 3x = -12
Eq1: 1.4x + 3y = -1.
Eq2: -3x + 2y = -12.
Multiply Eq1 by -2, Eq2 by 3, and add:
-2.8x - 6y = 2
-9x + 6y = -36
Sum: -11.8x = -34, X = 2.88.
In Eq1, replace X with 2.88 and solve for Y.
To solve the simultaneous equations 1.4x + 3y = -1 and 2y - 3x = -12, we can use the method of substitution or elimination. I will explain how to solve it using the elimination method.
First, we will eliminate one variable by multiplying one or both equations by suitable numbers so that the coefficients of one of the variables are additive inverses. In this case, we can multiply the second equation by 1.4 to make the coefficients of x in both equations multiples of 1.4. This will allow us to eliminate the x variable.
The given equations are:
1.4x + 3y = -1 (Equation 1)
2y - 3x = -12 (Equation 2)
Multiplying Equation 2 by 1.4:
1.4 * (2y - 3x) = 1.4 * (-12)
2.8y - 4.2x = -16.8 (Equation 3)
Now, we can eliminate the x variable by subtracting Equation 3 from Equation 1:
1.4x + 3y - (2.8y - 4.2x) = -1 - (-16.8)
1.4x + 3y - 2.8y + 4.2x = -1 + 16.8
(1.4x - 4.2x) + (3y - 2.8y) = 15.8
(-2.8x) + 0.2y = 15.8 (Equation 4)
Now we have a new equation where the x variable is eliminated. Let's simplify Equation 4:
-2.8x + 0.2y = 15.8
Now, we solve Equation 4 for y by isolating the y variable:
0.2y = 15.8 + 2.8x
y = (15.8 + 2.8x) / 0.2
y = 79 + 14x (Equation 5)
We now substitute the value of y from Equation 5 into either Equation 1 or Equation 2 to solve for x. Let's substitute it into Equation 1:
1.4x + 3(79 + 14x) = -1
1.4x + 237 + 42x = -1
43.4x + 237 = -1
43.4x = -238
x = -238 / 43.4
x ≈ -5.49
So, the solution to the simultaneous equations is x ≈ -5.49 and y = 79 + 14(-5.49) ≈ -63.66.