Question

Solve the following system of linear equations graphically: (3x + 2y = 6) and (x = 2y + 4). Use the strategy of y = mx + b.

a) ( (2,1) )
b) ( (1,2) )
c) ( (3,0) )
d) ( (0,3) )

Answer 1

The solution to the system of linear equations is given by option c) ( (3,0) ). (option c)

Step-by-step explanation:

To solve the system of linear equations 3x + 2y = 6 and x = 2y + 4 graphically, let's first rewrite both equations in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

For the first equation 3x + 2y = 6, rearrange to get y = -3/2x + 3, identifying the slope m as -3/2 and y-intercept b as 3.

For the second equation x = 2y + 4, rearrange to get y = 1/2x - 2, with slope m as 1/2 and y-intercept b as -2.

Now, graph these two lines on the coordinate plane. The point where the lines intersect is the solution to the system. In this case, the solution is (3,0), matching option c) ( (3,0) ).

Therefore, the correct graphical solution to the system of linear equations is (3,0).(option c)