Hi!
<u>Given these two equations:</u>
We want to solve using the substitution method. Knowing that x is equal to y + 8, we can simply plug in 'y + 8' in for x in the second equation, like so:
Combine like terms on both sides:
Subtract y from both sides:
Subtract 8 from both sides:
Now, we can simply plug the y value in to the first equation, and solve for x:
Simplify:
<u>Learn more about the substitution (and also elimination!) method here:</u>
Answer:
147.5 km and 64.4 km
Step-by-step explanation:
a=120 km
b=70 km
β=28 degrees ( ∘)
b^2=(a^2)+(c^2)−2ac*cosβ
70^2 =(120^2 )+(c^2)−2⋅ 120⋅ c⋅ cos(28∘ )
(c^2 ) −211.907c+9500=0
note p, q, and r are replacement variables in the Pythagorean theorem since a, b, and c are already in use
p=1;q=−211.907;r=9500
D=(q^2 ) −4pr=(211.907^2 )−4⋅1⋅9500=6904.75561996
D>0
=
(−q±
)/2p=(211.91±
)/2
=105.95371114±41.5474295834
(−147.501140726)(
−64.4062815596)=0
=147.501140726
=64.4062815596