Can anyone help without using reciprocal?
1 answer:
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Answer:
Equivalent systems of equations review
Step-by-step explanation:
We're given two systems of equations and asked if they're equivalent.
x + 4y = 8 (1)
4x + y = 2 (2)
Interestingly, if we sum the equations in System A, we get:
Replacing the first equation in System A with this new equation, we get a system that's equivalent to System A:
This is System B, which means that System A is equivalent to System B.
Well hmmm does the graph open upwards or downwards? well
is a quadratic, if the leading term's coefficient is negative, Down, if positive, Up
a)
now, let's see the leading term, -x², what's its coefficient? is -1 * x² or -1x², is -1, so is negative, thus is opening downwards
c)
x-intercepts occur, when y = 0, namely y = -x²-4x-3, so setting y to 0
0 = -x² -4x -3 take a common factor of -1, thus
0 = -1 (x²+4x+3) <--- now, if we factor that out, notice, surely you've done many of these by now, so we end up with
so, the x-intercepts are at -3 and -1
d)
now, the y-intercepts, just set x = 0
y = -x²-4x-3, settting x to 0 y = -0²-4(0)-3, which is y = -3
so the sole y-intercept is at y = -3
now, let's get on to b)
b)
and those are the coordinates, notice a = -1, b = -4 and c = -3
now, for
e)
well, all you have to do is, once you have the vertex, pick an x-value on the left-hand-side of the vertex, get they value for "y", or OUTPUT,
then pick another x-value, on the right-hand-side of the vertex, get the "y" value again, and plot away
is a quadratic, if the leading term's coefficient is negative, Down, if positive, Up
a)
now, let's see the leading term, -x², what's its coefficient? is -1 * x² or -1x², is -1, so is negative, thus is opening downwards
c)
x-intercepts occur, when y = 0, namely y = -x²-4x-3, so setting y to 0
0 = -x² -4x -3 take a common factor of -1, thus
0 = -1 (x²+4x+3) <--- now, if we factor that out, notice, surely you've done many of these by now, so we end up with
so, the x-intercepts are at -3 and -1
d)
now, the y-intercepts, just set x = 0
y = -x²-4x-3, settting x to 0 y = -0²-4(0)-3, which is y = -3
so the sole y-intercept is at y = -3
now, let's get on to b)
b)
and those are the coordinates, notice a = -1, b = -4 and c = -3
now, for
e)
well, all you have to do is, once you have the vertex, pick an x-value on the left-hand-side of the vertex, get they value for "y", or OUTPUT,
then pick another x-value, on the right-hand-side of the vertex, get the "y" value again, and plot away