given these equations:
x+y=9.0
0.5x+.2y=3.0
find the values of x and y
I would starb by getting rid of the decimals.
Multiply the second equation by 10
5x + 2y = 30
x + y = 9
multiply the bottom equation by -2
5x + 2y = 30
-2x -2y = -18
Add the two equations to get 3x = 12
so x = 4. Find y by substituting into one of the original equations.
then you should check your answers in both original equations.
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.
Step 1: Solve one equation for one variable.
From the first equation, we can rearrange it to solve for x:
x = 9.0 - y
Step 2: Substitute the expression for x into the other equation.
Replace x in the second equation with (9.0 - y):
0.5(9.0 - y) + 0.2y = 3.0
Step 3: Solve the resulting equation for y.
Distribute 0.5 to 9.0 and -y, then combine like terms:
4.5 - 0.5y + 0.2y = 3.0
-0.3y + 4.5 = 3.0
-0.3y = 3.0 - 4.5
-0.3y = -1.5
Step 4: Solve for y.
Divide both sides of the equation by -0.3 to isolate y:
y = -1.5 / -0.3
y = 5.0
Step 5: Substitute the value of y back into one of the original equations to solve for x.
Using the first equation:
x + y = 9.0
x + 5.0 = 9.0
x = 9.0 - 5.0
x = 4.0
Therefore, the solution to the system of equations is:
x = 4.0
y = 5.0