After the addition of an acid, a solution has a volume of 90 milliliters. The volume of the solution is 3 milliliters greater th
1 answer:
Answer:
Step-by-step explanation:
Let be "x" the original volume of the solution (in milliliters) before the acid was added and "y" the volume of the solution (in milliliters) after the addition of the acid.
Set up a system of equations:
Applying the Substitution Method, you can substitute the second equation into the first equation and then solve for "x":
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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