Question

How do you find the ordered pair that is a solution to the system of equations \[x + y = 10\] and \[x - y = 8\] ?

Answer 1

Hint: To solve a system of linear equations, we need to use the equations to obtain more equations from which values of the variable can be found out easily. The same needs to be done here. We can obtain two new equations by adding and subtracting the given equations one by one.

Complete step by step solution:
We have two equations. We need to find the value of x and y, so that we can generate the ordered pair which is the solution to the equations given above.
Recall that an ordered pair is simply the values of x and y written in \[(x,y)\] format. Thus, once we obtain the solution values of x and y, it will be easy to generate an ordered pair.
The equations are as follows:
  \[
  x + y = 10 \to (1) \\
  x - y = 8 \to (2) \;
 \]
Now, adding (1) and (2), we get
  \[
  x + y + x - y = 10 + 8 \\
  2x = 18 \\
  x = 9 \;
 \]
Thus, the value of x that is a solution to these equations is 9.
Now, on subtracting (1) and (2), we will get
  \[
  x + y - x + y = 10 - 8 \\
  2y = 2 \\
  y = 1 \;
 \]
Thus, the value of y that is a solution to these equations is 1.
Now that we have the solution values of x and y, we can generate the ordered pair.
The ordered pair obtained will be \[(9,1)\] , which is a solution to the system of equations \[x + y = 10\] and \[x - y = 8\] .
So, the correct answer is “ \[(9,1)\]”.

Note: A system of equations consists of a few equations which have as many variables as the total number of equations, or less. These equations are linked, and if one of them is solved, eventually all of them get solved.