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tej18
[6.03] What is the value of the y variable in the solution to the following system of equations? 2x + y = 5 x + 3y = 0 −1 1 3 −3
Let x = xylophones and y = yachts. Fred is buying xylophones and yachts. He does not pay attention to how much each costs, rather he just pays for all of them in one go. When he visits the shop on Monday, he buys two xylophones and one yacht for a total price of $9. He then thanks the salesman and goes home. The next day he buys three xylophones and four yachts for a total price of $26. Fred is now deeply curious as to how much his xylophones and yachts would have cost him individually, so he sets up a set of simultaneous equations in an attempt to find an answer to the ultimate question... 2x + y = 9 3x + 4y = 26 Transpose equation 1 and substitute into 2: y = 9 - 2x 3x + 4(9 - 2x) = 26 3x + 36 - 8x = 26 -5x = -10 x = 2 y = 9 - 4 y = 5 So it turns out that xylophones cost $2 each and yachts cost $5 each. ANSWERS: 3. Parallel 4. -6 + x 8. -1 9. (9, -1) 10. Multiply the first equation by -2 11. 42 12. 22.95 + 0.08m = 27.95 + 0.06m 13. 70 14. d = 3(r – 30) and d = 2(r + 30) 15. 3 hours 16. (5, 1) 17. Green area: 2x + y > 2 and x − y < 6 Yellow area: 2x + y > 2 and x − y > 6 18. Answer shown in part 2 (very long answer)
\[\large{\color{red}{2x+y=5}}\] \[\large{\color{blue}{\textbf{Solve for x in this eqn}}}\]
@tej18 what do you get after solving for x in 2x+y=5
OMG......... what is that @abayomi12
i dont get it @mathslover
2x+y=5 2x=5-y solve for x
teji u still don't get the answer that all the answer i just solved there
@mathslover so x= 5/2 - y/2??
x=(5-y)/2 put this in 2nd eqn
solve for y then you will get your answer
\[\large{x=\frac{5-y}{2}}\] \[\large{x+3y=0}\] \[\large{\frac{5-y}{2}+3y=0}\] \[\large{\frac{5-y+2y}{2}=0}\] \[\large{5+y=0}\]
oops sorry : \[\large{\frac{5-y+6y}{2}=0}\] \[\large{5+5y=0}\]
Answer: -1 2x+y=5 x+3y=0 So, x=-3y Substitute x=-3y into 2x+y=5 2(-3y)+y=5 -6y+y=5 -5y=5 y=-1