Solve the following systems graphically?

Question

a)

y = 2x + 3

y = 3x + 1

b)

2y – 4x = -2

3x + 6y = 21

Answer 1

to graph the lines  simply apply

y= mx+b

where m slope  b  is y intercept

a) y = 2x+ 3

m = 2, b= 3

m is slope = rise / run= 2/1(  slope to the right)

do  the same with second eqtn

m= 3, b= 1

when u graph u will see that they intersect  at ( 1,3)  which is the solution set

for letter B

just transform the equation to y = mx+b

follow the steps above.

Answer 2

a)  y = 2x +3 and y = 3x + 1

each equation is in the slope y-intercept form.

y = mx + b where m is the slope and (0,b) is the y-intercept

1st line can be graphed plotting (0,3) and the slope is the change in y over the change in x so 2 is 2/1 so change in y is 2 for each 1 change in x plot a second point (0+1,3+2) = (1,5) draw line through these 2 points

(0,3) and (1,5)

2nd line has slope=m=3 and y-intercept is (0,b)=(0,1)

plot (0,1) using the slope 3/1 finding a second point to  be (0+1, 1+3) = (1,4) plot this point and draw the line through (0,1) and (1,4)

find the point where the two lines intersect.  It should be close to (2,7).

b) 2y - 4x = -2 and 3x + 6y = 21

solve each equation for y

2y - 4x = -2 ==> 2y = 4x - 2 ==> y = 2x -1

3x + 6y = 21 ==> 6y = -3x + 21 ==> y = (-1/2)x + 7/2

using the same process as in problem a)

1st line has slope 2/1 and goes through (0,-1)

2nd line has slope -1/2 and goes through (0,7/2)

find 2nd point for 1st line as (0+1,-1+2) = (1,1)

find 2nd point for 2nd line as (0+2,7/2-1) = (2,5/2)

plot the two points for line and draw the line through them.

They should intersect at (9/5,13/5) = (1.8,2.6)