This is a 2-page document! Solve each system of equations by elimination Clearly identify your solution. 1. ) y=-x+1 y=4x-14

To solve the system of equations by elimination, we can add the two equations together to eliminate the variable $$y$$ .

Given:
$$y = -x + 1$$
$$y = 4x - 14$$

Step 1: Add the two equations together.
$$(-x + 1) + (4x - 14) = 0$$
$$-x + 4x + 1 - 14 = 0$$
$$3x - 13 = 0$$

Step 2: Solve for $$x$$ .
$$3x - 13 = 0$$
$$3x = 13$$
$$x = \frac{13}{3}$$

Step 3: Substitute the value of $$x$$ into one of the original equations to solve for $$y$$ .
Let's substitute $$x = \frac{13}{3}$$ into the first equation $$y = -x + 1$$ .
$$y = -\frac{13}{3} + 1$$
$$y = -\frac{13}{3} + \frac{3}{3}$$
$$y = -\frac{10}{3}$$

Therefore, the solution to the system of equations is:
$$x = \frac{13}{3}$$
$$y = -\frac{10}{3}$$