x+y=9.0
0.50x+0.20y=3.90
What is the value of x and y?
To find the values of x and y, we can solve the system of equations using the method of substitution or elimination. Let's use the method of substitution.
1. Start with the first equation:
x + y = 9.0
2. Solve this equation for x:
x = 9.0 - y
3. Substitute the value of x in the second equation:
0.50(9.0 - y) + 0.20y = 3.90
4. Simplify the equation:
4.50 - 0.50y + 0.20y = 3.90
5. Combine like terms:
0.30y = 3.90 - 4.50
6. Simplify further:
0.30y = -0.60
7. Divide both sides by 0.30:
y = -0.60 / 0.30
8. Calculate y:
y = -2
9. Substitute the value of y back into the first equation to find x:
x + (-2) = 9.0
x = 9.0 + 2
x = 11
The values of x and y are x = 11 and y = -2.
To solve this system of equations, we can use the method of substitution. We'll solve the first equation for x and then substitute it into the second equation.
From the first equation x + y = 9.0, we can rearrange it to get x = 9.0 - y.
Now, we'll substitute this expression for x into the second equation:
0.50(9.0 - y) + 0.20y = 3.90.
We can then solve for y:
4.5 - 0.50y + 0.20y = 3.90,
4.5 - 0.30y = 3.90,
-0.30y = 3.90 - 4.5,
-0.30y = -0.6.
Dividing both sides by -0.30, we get y = (-0.6)/(-0.30) = 2.0.
Now that we have the value of y, we can substitute it back into the first equation to find x:
x + 2.0 = 9.0,
x = 9.0 - 2.0,
x = 7.0.
Therefore, the solution to the system of equations is x = 7.0 and y = 2.0.
I would do this.
x+y = 9.0
0.50x + 0.20y = 3.90
------------------Multiply eqn 1 by -(1/2).
-0.50x - 0.50y = -4.50. keep eqn 2 as is.
0.50x + 0.20y = 3.90
-----------------------Now add the two. You see the x term cancels. Solve for y, then substitute y back into one of the equation and solve for x.