6. Solve the system of equations to find the value of x(+)y. Show all work. points) 5x+7y=1 x=-2y+2

## Step 1: Substitute $x$<br />### The second equation gives $x$ in terms of $y$. Substitute this expression for $x$ into the first equation. This gives $5(-2y + 2) + 7y = 1$.<br /><br />## Step 2: Simplify and solve for $y$<br />### Distribute the 5: $-10y + 10 + 7y = 1$. Combine like terms: $-3y + 10 = 1$. Subtract 10 from both sides: $-3y = -9$. Divide by -3: $y = 3$.<br /><br />## Step 3: Solve for $x$<br />### Substitute $y=3$ back into either of the original equations. Using the second equation, $x = -2(3) + 2 = -6 + 2 = -4$.<br /><br />## Step 4: Calculate $x+y$<br />### We have $x = -4$ and $y = 3$. Therefore, $x + y = -4 + 3 = -1$.