Question

equations: linear combinations
at what value of x do the graphs of the equations intersect?
2x - y = 6
5x + 10y = -10
options: 2, -2\frac{2}{3}, -2, 10\frac{2}{3}

Explanation:

Step1: Solve the first equation for y

From \(2x - y = 6\), we can rewrite it as \(y = 2x - 6\).

Step2: Substitute y into the second equation

Substitute \(y = 2x - 6\) into \(5x + 10y = -10\):
\[

$$\begin{align*} 5x + 10(2x - 6)&=-10\\ 5x + 20x - 60&=-10\\ 25x - 60&=-10 \end{align*}$$

\]

Step3: Solve for x

Add 60 to both sides:
\[

$$\begin{align*} 25x - 60 + 60&=-10 + 60\\ 25x&=50 \end{align*}$$

\]
Divide both sides by 25:
\[
x = \frac{50}{25}=2
\]

Answer:

2