If the y-intercepts are the same, the two equations represent the same line and there are INFINITELY MANY SOLUTIONS
Linear functions have to have the same slope between any 2 points
find the slope betwen them
slope betwen 2 points (x1,y1) and (x2,y2) is
(y1-y1)/(x2-x1)
given
(1,12) and (3,9)
slope=(9-12)/(3-1)=-3/2
if we wanted to chek furthere, we check (3,9) and (5,6) and fnd that the slope is also -3/2
so
y=mx+b
m=slope
b=yint
y=-3/2x+b
find b
if x=1 then y=12
12=-3/2+b
add 3/2 both sides
12+3/2=b
13+1/2=b
26/2+1/2=b
27/2=b
y=-3/2x+27/2
try them
we have 2 x values
7 and 3
input them and see their outputs
for x=7
y=-3/2(7)+27/2
y=-21/2+27/2
y=6/2
y=3
(7,3) is a valid point
for x=3
hold a second, we already have a x=3
it is (3,9)
none of them
answer is (7,3)
Expand by multiplying out:
14-15t + 36 = 1 -20t -1,
Because of the minus before the bracket, it changes the sign inside the bracket
-15t + 20t = 1-1-14-36 Rearranging the ts on one side and the numbers on other
side.
5t = -50 Divide both sides by 5.
t = -50/5
t = -10.
The equation given in the question has to be answered to the nearest tenth. The only thing that one should be careful about is the cross multiplication part. Other than that there is no difficulty in the given problem. Now let us get down to the equation in the question.
15/30 = n/34
30 * n = 15 * 34
30n = 510
n = 510/30
= 51/3
= 17
So the value of the unknown variable "n" comes out to be 17.
