Solve the pair of linear equations: x + $y = 14$ and x - $y = 4$ .

Answer: The solution to the pair of linear equations is $x = 9$ and $y = 5$ .

Step-by-step solution

Step 1: Write down the given equations

We are given two linear equations with two variables, $x$ and $y$ . We need to find the values of $x$ and $y$ that satisfy both equations simultaneously.

Step 2: Add the two equations

We can eliminate one of the variables by adding the two equations. Notice that the $y$ terms have opposite signs ( $+y$ and $-y$ ), so they will cancel out when added. Adding the left sides gives $(x+y) + (x-y) = 2x$ , and adding the right sides gives $14+4=18$ .

Step 3: Solve for x

Now we have a simple linear equation with only one variable, $x$ . To find the value of $x$ , we divide both sides of the equation by 2. This gives us $x = 9$ .

Step 4: Substitute x into one of the original equations

We now know the value of $x$ . We can substitute this value into either Equation 1 or Equation 2 to find $y$ . Let's use Equation 1. Substituting $x=9$ into $x+y=14$ gives us $9+y=14$ .

Step 5: Solve for y

To solve for $y$ , subtract 9 from both sides of the equation. This gives us $y = 5$ . We have now found the values for both $x$ and $y$ .

Step 6: Verify the solution

It's always a good practice to verify the solution by substituting the values of $x$ and $y$ back into both original equations. For Equation 1, $9+5=14$ , which is correct. For Equation 2, $9-5=4$ , which is also correct. Thus, our solution is verified.

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Solve the pair of linear equations: x + y=14y = 14y=14 and x - y=4y = 4y=4.