Question

Graph both equations to find the solutionfor this system.y = 2x - 9 y = -1/2x + 1

Answer 1

Recall that to graph a line, we need only two points.

Substituting x=0 and x=4.5 in the first equation we get:

$\begin{gathered} y=2\cdot0-9=-9, \\ y=2\cdot4.5-9=9-9=0. \end{gathered}$

Therefore the graph of the first equation is a straight line that passes through (0,-9) and (4.5,0).

Substituting x=0 and x=2 in the second equation we get:

$\begin{gathered} y=-\frac{1}{2}\cdot0+1=0+1=1, \\ y=-\frac{1}{2}\cdot2+1=-1+1=0. \end{gathered}$

Therefore the graph of the second equation is a straight line that passes through (0,1) and (2,0).

The graph of both equations is:

From the above graph, we get that the solution to the given system of equations is:

$(4,-1)$

Answer:

The solution of the given system of equations is x=4 and y=-1.