By using the elimination method, you would essentially add the two equations together by combining like terms. normally this would require manipulation however this equation doesn't because the y is already opposites of each other. (a negative and positive value of the same number i.e. -2 and 2)
so add the two equations together and you're left with 2x = 16, (they y's cancelled each other out) then divide two on both sides to get x = 8
now, use that x value in either equation (it doesn't matter which), we can use -3x+2y=-26
plug it in to get -3(8) + 2y = -26
which is then -24 + 2y = -26
add 24 to both sides: 2y = -2
divide 2 on both sides: y = -1
now knowing x=8 and y= -1 we can say that the answer is (8,-1)
hope this helps!!
Answer:
The horizontal asymptote is y=0
Answer:
Step-by-step explanation:
When the coefficients don't lend themselves to solution by substitution or elimination, then Cramer's Rule can be useful. It tells you the solutions to
are ...
- ∆ = bd -ea
- x = (bf -ec)/∆
- y = (cd -fa)/∆
Using that rule here, we find ...
∆ = 5·3 -6·2 = 3
a = (5·54 -6·41)/3 = 5·18 -2·41 = 90 -82 = 8
s = (41·3 -54·2)/3 = 41 -18·2 = 5
This math can be performed in your head, which is the intent of formulating the rule in this way.
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Similarly, if you expect the solutions to be small integers (as here), then graphing is another viable solution method.
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<em>Comment on the question</em>
We're sad to see than only 16 tickets were sold to the two performances by the symphonic band.
Move all variables to the left side and all constants to the right side.<span><span><span><span>(x−2)</span>2</span>+<span>y2</span>=64</span><span><span><span>(x-2)</span>2</span>+<span>y2</span>=64</span></span>This is the form of a circle. Use this form to determine the center and radius of the circle.<span><span><span><span>(x−h)</span>2</span>+<span><span>(y−k)</span>2</span>=<span>r2</span></span><span><span><span>(x-h)</span>2</span>+<span><span>(y-k)</span>2</span>=<span>r2</span></span></span>Match the values in this circle to those of the standard form. The variable <span>rr</span> represents the radius of the circle, <span>hh</span> represents the x-offset from the origin, and <span>kk</span> represents the y-offset from origin.<span><span>r=8</span><span>r=8</span></span><span><span>h=2</span><span>h=2</span></span><span><span>k=0</span><span>k=0</span></span>The center of the circle is found at <span><span>(h,k)</span><span>(h,k)</span></span>.Center: <span><span>(2,0)</span><span>(2,0)</span></span>These values represent the important values for graphing and analyzing a circle.Center: <span><span>(2,0)</span><span>(2,0)</span></span>Radius: <span>8</span>
Make a proportion
81/30 = x/600
600/30 = 20
x/81 = 20
x = 1620
Solution: 1620 calories
