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.### Let 'x' and 'y' represent the two numbers. The sum of the numbers is 1, which translates to the equation . The difference of the numbers is 11, which translates to the equation .## Step 2: Solve for x using the second equation.### Isolate x in the second equation: . Adding y to both sides gives .## Step 3: Substitute the value of x into the first equation.### Substitute into the first equation . This gives .## Step 4: Solve for y.### Simplify the equation from Step 3: . Subtract 11 from both sides: . Divide both sides by 2: .## Step 5: Substitute the value of y back into either original equation to solve for x.### Substitute into the equation . This gives , so .