Question

1. does diego’s method work for solving these systems? be prepared to explain or show your reasoning.

system of linear equations	does diegos method work? why or why not?	solve the system

| a. \\(\

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

\\) | | |

Explanation:

Step1: Add the two equations

$$(2x + y) + (x - y) = 4 + 11$$
$$3x = 15$$

Step2: Solve for $x$

$$x = \frac{15}{3} = 5$$

Step3: Substitute $x=5$ into $x-y=11$

$$5 - y = 11$$

Step4: Solve for $y$

$$-y = 11 - 5 = 6$$
$$y = -6$$

Step5: Verify validity

This method works because adding the equations eliminates the $y$-variable, which is a standard elimination method for linear systems, and the solution satisfies both original equations.

Answer:

Yes, Diego's method (elimination) works. The solution is $x=5$, $y=-6$.