Question: 7. $(-2, 1)$; $6x + 5y = -7$ $2x - 4y = -8$ In Exercises 9-12, use the graph of the linear…

7. $(-2, 1)$; $6x + 5y = -7$ $2x - 4y = -8$

In Exercises 9-12, use the graph of the linear equations. Check your solution.

9. $x - y = 4$ $4x + y = 1$

[Graph of two lines intersecting at a point]

Solution

We need to solve the following system of linear equations: \[ \begin{cases} x - y = 4 & \\ 4x + y = 1 & \end{cases} \] First, solve the first equation for \(x\): \[ x = y + 4 \] Substitute \(x = y + 4\) into the second equation: \[ 4(y + 4) + y = 1 \] Simplify and solve for \(y\): \[ 4y + 16 + y = 1 \] \[ 5y + 16 = 1 \] \[ 5y = 1 - 16 \] \[ 5y = -15 \] \[ y = -3 \] Substitute \(y = -3\) back into \(x = y + 4\) to find \(x\): \[ x = -3 + 4 \] \[ x = 1 \] The solution to the system is \(x = 1\) and \(y = -3\).