How to prove system of nonlinear equations has finite solutions?
1 answer:
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a) x – 2y + 6 = 0 b) x + y = 1 c) y = 1 d) y = -3x + 8
<h3><u>Solution:</u></h3><em><u>a. The points (-4,1) and (2,4) both lie on the line</u></em>
The general line equation on which (a, b) and (c, d) lies is:
Here the given points are (a, b) = (-4, 1) and (c, d) = (2, 4)
Thus the required equation is:
On solving we get,
<em><u>b.) m= -1 and the point (2, -1) lies on the line</u></em>
The equation of line in point slope form is y – b = m(x – a)
where m is slope and (a, b) is a point on it
Here m = -1 and (a, b) = (2, -1)
Thus the required equation is:
y – (-1) = -1(x - 2)
y + 1 = -x + 2
y = -x + 2 -1
y = -x + 1
<em><u>c. )It has the same slope as y = 5 and passes through (1, 1)</u></em>
our line has same slope with y = 5, then our equation would be y = k and it passes through (x, y) = (1, 1) so, then by substitution
1 = k
k =1
Then our equation will be y = k
y = 1
<em><u> d. ) m= -3 and it has a y-intercept of (0, 8)</u></em>
line equation in slope intercept form is y = mx + b where m is slope and b is y – intercept.
Then, our equation will be y = -3x + 8
We took y- intercept = 8 as it is the value of y when x = 0