3. The numbers x and y have a sum of 1 and a difference of II. (1) a. Write a system of equations to represent this information. Lesson 8.2: Solving Systems of Linear Equations by Substitution Workbook 82 b. Solve the system of equations to determine the numbers. ADLC] Mathematics 10C

## Step 1: Define the variables and set up the equations.<br />### Let 'x' and 'y' represent the two numbers. The sum of the numbers is 1, which translates to the equation $x + y = 1$. The difference of the numbers is 11, which translates to the equation $x - y = 11$.<br /><br />## Step 2: Solve for x using the second equation.<br />### Isolate x in the second equation: $x - y = 11$. Adding y to both sides gives $x = y + 11$.<br /><br />## Step 3: Substitute the value of x into the first equation.<br />### Substitute $x = y + 11$ into the first equation $x + y = 1$. This gives $(y + 11) + y = 1$.<br /><br />## Step 4: Solve for y.<br />### Simplify the equation from Step 3: $2y + 11 = 1$. Subtract 11 from both sides: $2y = -10$. Divide both sides by 2: $y = -5$.<br /><br />## Step 5: Substitute the value of y back into either original equation to solve for x.<br />### Substitute $y = -5$ into the equation $x = y + 11$. This gives $x = -5 + 11$, so $x = 6$.