Question

write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. there are two mystery numbers. the sum of 8 times the first number and 6 times the second number is 44. the sum of 3 times the first number and 8 times the second number is 28. what are the two numbers? the first number is \boxed{}, and the second number is \boxed{}. save answer

Explanation:

Step1: Define variables

Let the first number be $x$, the second be $y$.

Step2: Write system of equations

$$\begin{cases} 8x + 6y = 44 \\ 3x + 8y = 28 \end{cases}$$

Step3: Eliminate $x$ (scale equations)

Multiply first eq by 3: $24x + 18y = 132$
Multiply second eq by 8: $24x + 64y = 224$

Step4: Subtract equations

$(24x + 64y) - (24x + 18y) = 224 - 132$
$46y = 92$

Step5: Solve for $y$

$y = \frac{92}{46} = 2$

Step6: Substitute $y=2$ to find $x$

$8x + 6(2) = 44$
$8x + 12 = 44$
$8x = 32$
$x = \frac{32}{8} = 4$

Answer:

The first number is 4, and the second number is 2.