Question

mira picked two numbers from a bowl. the difference of the two numbers was 4, and the sum of one - half of each number was 18. the system that represents miras numbers is shown.
$x - y = 4$
$\frac{1}{2}x+\frac{1}{2}y = 18$
which two numbers did mira pick?
18 and 4
40 and 32
10 and 8
20 and 16

Explanation:

Step1: Simplify the second equation

The second equation is \(\frac{1}{2}x+\frac{1}{2}y = 18\). Multiply both sides by 2 to eliminate the fractions: \(x + y=36\).

Step2: Solve the system of equations

We have the system:
\[

$$\begin{cases} x - y=4\\ x + y=36 \end{cases}$$

\]
Add the two equations together: \((x - y)+(x + y)=4 + 36\), which simplifies to \(2x=40\). Then divide both sides by 2: \(x = 20\).

Step3: Find the value of y

Substitute \(x = 20\) into the first equation \(x - y=4\): \(20 - y=4\). Subtract 20 from both sides: \(-y=4 - 20=-16\). Multiply both sides by - 1: \(y = 16\).

Answer:

20 and 16