Given These Equations
x+y=9.0
.50x+.20y=3.90
Find the values of X and Y.
Would multiplying the 2nd equation by 10 to get
5x + 2y = 39 make it any easier?
10x+20y-30z
To solve for the values of x and y, we can use the method of substitution or elimination. Let's use the method of substitution.
Step 1: Solve the first equation for either variable. Let's solve for x in terms of y:
x = 9.0 - y
Step 2: Substitute the expression for x in the second equation:
0.50(9.0 - y) + 0.20y = 3.90
Step 3: Distribute and solve for y:
4.50 - 0.50y + 0.20y = 3.90
Combine like terms: -0.50y + 0.20y = 3.90 - 4.50
-0.30y = -0.60
y = -0.60 / -0.30
y = 2
Step 4: Substitute the value of y back into the first equation to solve for x:
x + 2 = 9.0
x = 9.0 - 2
x = 7
Therefore, the values of x and y are:
x = 7
y = 2
To find the values of x and y, we can use a method called "substitution" or "elimination" to solve the system of equations.
Let's start with the first equation:
x + y = 9.0 ...(Equation 1)
Now, let's rearrange Equation 1 to solve for x:
x = 9.0 - y ...(Equation 2)
Next, we can substitute this value of x into the second equation:
0.50x + 0.20y = 3.90 ...(Equation 3)
Substituting Equation 2 into Equation 3:
0.50(9.0 - y) + 0.20y = 3.90
Now, let's simplify and 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 = -0.60
y = -0.60 / -0.30
y = 2
Now that we have the value of y, we can substitute it back into Equation 2 to find the value of x:
x = 9.0 - y
x = 9.0 - 2
x = 7
Therefore, the solutions to the system of equations are:
x = 7 and y = 2.