Solve the following system of linear equations by graphing: \[ \begin{array}{r}-4 x+y=6 \\ -2 x+y=6\end{array} \]

To solve the system of equations by graphing, let's first rearrange each equation into slope-intercept form (y = mx + b). 1. For the first equation, \(-4x + y = 6\): \[ y = 4x + 6 \] 2. For the second equation, \(-2x + y = 6\): \[ y = 2x + 6 \] Now, let's plot both equations on the same graph. - The first equation \(y = 4x + 6\) has a y-intercept of 6; when \(x = 0\), \(y = 6\). To find another point, let \(x = -1\): \[ y = 4(-1) + 6 = 2 \] So the points (0, 6) and (-1, 2) can be marked. - The second equation \(y = 2x + 6\) also has a y-intercept of 6. When \(x = 0\), \(y = 6\). Let's find another point by letting \(x = -2\): \[ y = 2(-2) + 6 = 2 \] So the points (0, 6) and (-2, 2) can be marked. When you graph these lines, they both intersect at the point (0, 6). Thus, the solution to the system of equations is: \(x = 0\) and \(y = 6\), or simply the point \((0, 6)\).