solving using the elimination method
0.3x-0.2y=4
0.2x+0.3y=5/23
To solve the given system of equations using the elimination method, follow these steps:
Step 1: Multiply the equations by appropriate coefficients to make the coefficients of one of the variables opposite in signs.
In this case, if we multiply the first equation by 10 and the second equation by 15, the coefficients of 'x' will become opposite in signs.
Multiplying the first equation by 10:
10(0.3x - 0.2y) = 10(4)
3x - 2y = 40 (Equation 1)
Multiplying the second equation by 15:
15(0.2x + 0.3y) = 15(5/23)
3x + 4.5y = 15/23 (Equation 2)
Step 2: Add the two equations together to eliminate one of the variables.
Adding Equation 1 and Equation 2:
(3x - 2y) + (3x + 4.5y) = 40 + 15/23
6x + 2.5y = 40 + 15/23
Simplifying the equation:
6x + 2.5y = 920/23 + 15/23
6x + 2.5y = 935/23 (Equation 3)
Step 3: Solve for the remaining variable.
Using Equation 3, isolate 'y':
2.5y = 935/23 - 6x
y = (935 - 6(23)x) / (23 * 2.5)
y = (935 - 138x) / 57
Step 4: Substitute the value of 'y' back into either Equation 1 or Equation 2 to solve for 'x'.
Let's substitute the value of 'y' into Equation 1:
3x - 2((935 - 138x) / 57) = 40
Now solve for 'x'.
Step 5: After finding the value of 'x', substitute it back into Equation 1 or Equation 2 to solve for 'y'.
Once you have the value of 'x', substitute it back into Equation 3 to solve for 'y'.
And that's how you solve the given system of equations using the elimination method.
.9x - .6y = 12
.4x + .6y = 10/23
Add the two.
1.3x = 12 10/23
You should be able to work it from here.