Question

SOLVING LINEAR EQUATIONS BY GRAPHINGdecide weather the ordered pair is a solution of the linear equations 3x – 2y = 11 -x + 6y=7 (5,2)

Answer 1

To graph a line we need to points. For simplicity we are going to use the intercepts of each of the equations.

For the equation 3x-2y=11 we notice that when y=0, we have:

`\begin{gathered} 3x=11 \\ x=(11)/(3) \end{gathered}`

then we have the point (11/3,0), this is the x-intercept of the line. Now to find the y-intercept we plug x=0 and solve for y, then we have:

`\begin{gathered} -2y=11 \\ y=-(11)/(2) \end{gathered}`

then we have the point (0,-11/2), Now that we have two points we draw them on the plane and join them wiht a straight line, then we have:

We do the same to find the graph for the second equation -x+6y=7. If y=0, then:

`\begin{gathered} -x=7 \\ x=-7. \end{gathered}`

then we have the point (-7,0). If x=0, then:

`\begin{gathered} 6y=7 \\ y=(7)/(6) \end{gathered}`

then we have the point (0,7/6). Once again we plot this points and join them wiht a straight line:

Once we have the graphj of both equations the solution of the system is the point of intersection between them. From the graph we notice that the intersection happens at the point (5,2), therefore the point is a solution to the system.