Think of two equations that are satisfied by the given point.
Example Solution: 2x+3y=20 4x+2y=16
Practice makes perfect
We want to write a system of linear equation that has the ordered pair (1,6) as its solution. To do so, we need to think of two equations that are satisfied by the given point.
? x+? y=? & (I) ? x+? y=? & (II)
Let's choose coefficients of x and y in both equations. Since we want system to have one solution we should not choose the same coefficients for both equations.
2x+3y=? 4x+2y=?
Now, to evaluate right-hand side for each equation we should substitute ( 1, 6) for x and y into the left-hand side and simplify. By doing this, we make sure that each equation is satisfied with the given point.
Equation 1
Equation 2
Substitute
2( 1)+3( 6)
4( 1)+2( 6)
Multiply
2+18
4+12
Add
20
16
Finally we can complete our system. Keep in mind that this is just one possible answer for this situation.
2x+3y= 20 4x+2y= 16
Checking Our Answer
Checking Our Solution
Let's check if our example system has a solution of (1,6). To do this, let's solve our system by substitution. We will start by solving Equation 2 for y.
