5x-2y=126x+2y=32find the solution
1 answer:
Answer:
(4,4)
Step-by-step explanation:
There are two ways that you can solve this. You can solve it with the help of technology or you can solve it traditionally. I will show how to do it in both ways so you can pick which way you want to solve it.
<em>Traditional Method:</em>
5x - 2y = 12
6x + 2y = 32
Look at the variables and numbers in both equations. One of them has to be the same value but have to have opposite signs. The 2y in both equations are the same value but have different signs. That's what we want. We can add everything in the equation now. (5x + 6x), (-2y + 2y), and (12 + 32).
11x = 44
To get x alone, Divide each side by 11. Then we will get the value of x.
11/11x = 44/11
x = 4
Horray! We got x, but what about y? Pick one of the equations. I will go with 5x - 2y = 12. Substitute the x value inside the equation.
5(4) - 2y = 12
20 - 2y = 12
-2y = -8
y = 4
Good! We figured out y. Now we know the solution! The solution is (4,4).
<em>Technology Method:</em>
Grab a graphing calculator. Enter the equations. You will see two lines. Look at where they intersect. The point where they intersect is the solution. That line is (4,4). You could also do this on a piece of paper by graphing the equations.
I hope this helps! Let me know if you need any more help or if I got anything wrong.
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Answer: B) different y intercepts; same end behavior
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Explanation:
The graph shows the y intercept is 4 as this is where the green curve crosses the vertical y axis.
The y intercept of g(x) is 6 which can be found by plugging x = 0 into the g(x) function
g(x) = 4(1/4)^x + 2
g(0) = 4(1/4)^0 + 2
g(0) = 6
So we can see the y intercepts are different.
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However, the end behaviors are the same for each function. The left side of f(x) goes up forever to positive infinity. The same is true for g(x). You could use a graphing calculator or a table to see this. As x heads to negative infinity, y goes to positive infinity.
In terms of symbols,
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For the right side of f(x), it slowly approaches the horizontal asymptote y = 2. It never actually reaches this y value. The same happens with g(x). The portion 4(1/4)^x gets smaller but never gets to 0 so overall 4(1/4)^x+2 gets closer to 2. We can say that as x approaches infinity, y approaches 2.
In terms of symbols,