.50x+.20y=3.60
x+y=9
0. 50 x + 0.20 y = 3.60 Multiply both sides by 2
x + 0.4 y = 7.2
x + 0.4 y = 7.2
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x + y = 9
_____________
0 - 0.6 y = - 1.8
- 0.6 y = - 1.8 Divide both sides by - 0.6
y = - 1.8 / - 0.6 = 3
y = 3
x + y = 9
x = 9 - y = 9 - 3 = 6
x = 6 , y = 3
To solve the system of equations:
Equation 1: 0.50x + 0.20y = 3.60
Equation 2: x + y = 9
We will solve this system using the substitution method.
Step 1: Solve equation 2 for x.
x = 9 - y
Step 2: Substitute the value of x from equation 2 into equation 1.
0.50(9 - y) + 0.20y = 3.60
Step 3: Simplify the equation.
4.50 - 0.50y + 0.20y = 3.60
Step 4: Combine like terms.
4.50 - 0.30y = 3.60
Step 5: Subtract 4.50 from both sides of the equation.
-0.30y = 3.60 - 4.50
Step 6: Simplify the equation.
-0.30y = -0.90
Step 7: Divide both sides of the equation by -0.30 to solve for y.
y = -0.90 / -0.30
Step 8: Simplify the equation.
y = 3
Step 9: Substitute the value of y into equation 2 to solve for x.
x + 3 = 9
Step 10: Subtract 3 from both sides of the equation.
x = 9 - 3
Step 11: Simplify the equation.
x = 6
Therefore, the solution to the system of equations is x = 6 and y = 3.
To solve this system of equations:
1. Start by solving the second equation for x or y. Let's solve it for x:
x = 9 - y
2. Substitute the value of x obtained in step 1 into the first equation:
0.50(9 - y) + 0.20y = 3.60
3. Distribute the 0.50 to the terms inside the parentheses:
4.50 - 0.50y + 0.20y = 3.60
4. Combine like terms:
4.50 - 0.30y = 3.60
5. Move the constant term to the other side of the equation:
-0.30y = 3.60 - 4.50
6. Simplify the right side of the equation:
-0.30y = -0.90
7. Divide both sides of the equation by -0.30 to solve for y:
y ≈ (-0.90)/(-0.30)
y ≈ 3
8. Substitute the value of y obtained in step 7 into either of the original equations (let's use the second equation) to solve for x:
x + 3 = 9
x ≈ 9 - 3
x ≈ 6
The solution to this system of equations is x ≈ 6 and y ≈ 3.