Question

ns using substitution or elimination. make sure each problem, as well as circle the number of , please also clearly identify the solution. mination substitution elimination c. \\((- 2x - 5y = 24)2\\) \\(8x + 10y =- 16\\)

Explanation:

Step1: Multiply the first equation by 2

We have the system of equations:
\[

$$\begin{cases} -2x - 5y = 24 \quad (1)\\ 8x + 10y = -16 \quad (2) \end{cases}$$

\]
Multiply equation \((1)\) by \(2\):
\(2\times(-2x - 5y)=2\times24\)
\(-4x - 10y = 48\quad(1)'\)

Step2: Add the new equation to the second equation

Add \((1)'\) and \((2)\):
\((-4x - 10y)+(8x + 10y)=48+(-16)\)
Simplify the left - hand side: \(-4x - 10y+8x + 10y = 4x\)
Simplify the right - hand side: \(48-16 = 32\)
So we get \(4x=32\)

Step3: Solve for x

Divide both sides of \(4x = 32\) by \(4\):
\(x=\frac{32}{4}=8\)

Step4: Substitute x = 8 into one of the original equations

Substitute \(x = 8\) into equation \((1)\): \(-2\times8-5y=24\)
Simplify: \(-16 - 5y=24\)
Add \(16\) to both sides: \(-5y=24 + 16=40\)
Divide both sides by \(-5\): \(y=\frac{40}{-5}=-8\)

Answer:

The solution of the system of equations \(

$$\begin{cases}-2x - 5y = 24\\8x + 10y=-16\end{cases}$$

\) is \(x = 8,y=-8\) or the ordered pair \((8,-8)\)