A geometric sequence such that ...
We can use the ratio of the given terms to find the common ratio of the sequence, then use that to find the desired term from one of the given terms. We don't actually need the common ratio (-2). All we need is its cube (-8).
The two solutions for the system of equations:
y = x^2+ 5x - 3
y - x = 2
Are:
(-5, -7) and (1, -1)
<h3>How to solve the system of equations?</h3>Here we have the following system of equations:
y = x^2+ 5x - 3
y - x = 2
We can replace the first equation into the second one to get:
(x^2+ 5x - 3) - x = 2
x^2 + 4x - 3 = 2
x^2 + 4x - 3 - 2 = 0
x^2 + 4x - 5 = 0
Using the quadratic formula, we will get the solutions:
The two solutions are:
x = (-4 - 6)/2 = -5
x = (-4 + 6)/2 = 1
To find the values of y, we can evaluate the linear equation:
when x = -5
y - (-5) = -2
y + 5 = -2
y = -2 - 5 = -7
So one solution is (-5, -7)
when x = 1
y - 1 = -2
y = -2 + 1 = -1
The other solution is (1, -1)
Learn more about systems of equations:
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