Question

at what value of x do the graphs of the equations below intersect?
2x - y = 6
5x + 10y = -10
\\( -2\frac{2}{3} \\)
-2
2
\\( 10\frac{2}{3} \\)

Explanation:

Step1: Isolate y from first equation

Rearrange $2x - y = 6$ to solve for $y$:
$y = 2x - 6$

Step2: Substitute y into second equation

Replace $y$ in $5x + 10y = -10$:
$5x + 10(2x - 6) = -10$

Step3: Expand and simplify the equation

Calculate the expanded form and combine like terms:
$5x + 20x - 60 = -10$
$25x - 60 = -10$

Step4: Solve for x

Isolate the variable $x$:
$25x = 60 - 10$
$25x = 50$
$x = \frac{50}{25} = 2$

Answer:

2 (Option C: 2)