i need the answers to this. Help is needed.

Question

Solve the system of linear equations by graphing.

y=12x+3

y=x+1



Answer 1

This is a great example of why you do NOT want to solve equations graphically.

Here is a graph of the two equations:

Can you see where the lines intersect? It appears it is a little less than zero in the x-direction and a little less than 1 in the y-direction. But unless you blow up the graph, Which, by the way you can do quite nicely on a graphing calculator or on desmos, you can't tell where the intersection is exactly.

Answer 2

Start by graphing each line individually. The first line is y=12x+3. This line has y-intercept (0,3) and x-intercept (-1/4,0). Plot these two points and connect them to form a line. Do the same thing with the second equation, y=x+1. This line has y-intercept (0,1) and x-intercept (-1,0). Plot these two points and connect them to form a line. Now to solve the system of equation, observe the point where those 2 lines intersect.

Answer 3

x=-2/11

y=9/11

the 1st equation has a slope = 1, a 45 degree upward sloping line with y intercept = 1

the 2nd equation has slope = 12, upward sloping but almost vertical, and y intercept = 3

their intersection is the point (-2/11, 9/11)

set 12x+3 = x+ 1, solve for x

11x =-2

x = -2/11

y=x+1 = -2/11 + 1 = 9/11