Question

1.12) \\(\

$$\begin{cases}-x + 4y = 6 \\\\ 2x - y = -5\\end{cases}$$

\\) and a coordinate grid with two lines plotted

Explanation:

Step1: Solve the system of equations

We have the system:

$$
LATEXBLOCK0
$$

From the second equation \(2x - y = -5\), we can express \(y\) in terms of \(x\): \(y = 2x + 5\).

Substitute \(y = 2x + 5\) into the first equation:

$$
LATEXBLOCK1
$$

Now substitute \(x = -2\) into \(y = 2x + 5\):

$$ y = 2(-2) + 5 = -4 + 5 = 1 $$

Step2: Find the intersection point on the graph

The solution to the system of linear equations is the point where the two lines intersect. From the graph, we can see that the two lines intersect at the point \((-2, 1)\), which matches the solution we found algebraically.

Answer:

The solution to the system of equations (the intersection point) is \((-2, 1)\)