solve using the elimination method
0.05x+0.25y=11
0.15x+0.05y=12
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Thank you this is what I was looking for just something to refer too!
You're very welcome.
To solve the given system of equations using the elimination method, follow these steps:
1. Multiply both equations by the necessary values to make the coefficients of either x or y in one equation equal but with opposite signs.
Multiply Equation 1 by 20 to eliminate the decimals:
(0.05x * 20) + (0.25y * 20) = 11 * 20
Simplify: x + 5y = 220 -- Equation 3
Multiply Equation 2 by 20 to eliminate the decimals:
(0.15x * 20) + (0.05y * 20) = 12 * 20
Simplify: 3x + y = 240 -- Equation 4
2. Now, we have a system of two equations:
Equation 3: x + 5y = 220
Equation 4: 3x + y = 240
3. Multiply Equation 3 by -3 (to get -3x) and Equation 4 by 1 (to get x):
-3(x + 5y) = -3 * 220
Simplify: -3x - 15y = -660 -- Equation 5
1(3x + y) = 1 * 240
Simplify: 3x + y = 240 -- Equation 4 (rewritten)
4. Add Equation 4 and Equation 5 together to eliminate x:
(-3x - 15y) + (3x + y) = -660 + 240
Simplify: -14y = -420
5. Solve for y:
Divide both sides of the equation (-14y = -420) by -14:
y = (-420)/(-14)
Simplify: y = 30
6. Substitute the value of y (y = 30) back into either Equation 3 or Equation 4 to find x. Let's use Equation 3:
x + 5(30) = 220
Simplify: x + 150 = 220
Subtract 150 from both sides:
x = 220 - 150
Simplify: x = 70
7. So, the solution to the system of equations is:
x = 70 and y = 30.
Therefore, the values of x and y are 70 and 30, respectively, in order to satisfy both equations.