Question

question 27 of 29
consider the system of linear equations.
x + y = 9.0
0.50x + 0.20y = 3.30
find the values of x and y.
x =
y =

Explanation:

Step1: Solve for y from first equation

From \( x + y = 9.0 \), we get \( y = 9.0 - x \).

Step2: Substitute y into second equation

Substitute \( y = 9.0 - x \) into \( 0.50x + 0.20y = 3.30 \):
\( 0.50x + 0.20(9.0 - x) = 3.30 \)
Expand: \( 0.50x + 1.8 - 0.20x = 3.30 \)
Combine like terms: \( 0.30x + 1.8 = 3.30 \)
Subtract 1.8: \( 0.30x = 3.30 - 1.8 = 1.5 \)

Step3: Solve for x

Divide by 0.30: \( x = \frac{1.5}{0.30} = 5 \)

Step4: Solve for y

Substitute \( x = 5 \) into \( y = 9.0 - x \): \( y = 9.0 - 5 = 4 \)

Answer:

\( x = 5 \)
\( y = 4 \)