Question

1. solve by elimination \\(\

$$\begin{cases} 2x - 5y = 11 \\\\ 4x + 10y = 18 \\end{cases}$$

\\)

Explanation:

Step1: Multiply the first equation

To eliminate a variable, we can multiply the first equation \(2x - 5y = 11\) by 2. This gives us \(4x - 10y = 22\).

Step2: Add the two equations

Now we have the two equations: \(4x - 10y = 22\) (from step 1) and \(4x + 10y = 18\) (the original second equation). Add them together: \((4x - 10y)+(4x + 10y)=22 + 18\). Simplifying the left side, the \(-10y\) and \(+10y\) cancel out, so we get \(8x=40\).

Step3: Solve for x

Divide both sides of \(8x = 40\) by 8: \(x=\frac{40}{8}=5\).

Step4: Substitute x back to find y

Substitute \(x = 5\) into the first original equation \(2x - 5y = 11\). So \(2(5)-5y = 11\), which simplifies to \(10 - 5y = 11\). Subtract 10 from both sides: \(-5y=11 - 10 = 1\). Then divide both sides by -5: \(y=\frac{1}{-5}=-\frac{1}{5}\).

Answer:

The solution to the system of equations is \(x = 5\) and \(y=-\frac{1}{5}\), or the ordered pair \((5,-\frac{1}{5})\).