Question

the instructions state..." here is a system of equations. y=2x+3 y=x-1graph the system. then write its solution. note that you can also answer "no solution" or "infinitely many" solutions."

Answer 1

To graph the system we need to find two points for each equation. To do this we give values to x and then find the corresponding values for y.

Equation y=2x+3:

If x=0 then y=3. Hence we have the point (0,3)

If x=1 theny=5. Hence we have the point (1,5)

Now we plot the points in the plane and join them with a line:

Equation y=x-1:

If x=0 then y=-1. Hence we have the point (0,-1)

If x=1 theny=0. Hence we have the point (1,0)

Now we plot the points in the plane and join them with a line:

Now, the solution of the system is the point where the lines intersect. From the graph we notice that this point is (-4,-5)

Therefore the solution is x=-4 and y=-5.