SOLUTION: Find values for h and k so that the system has infinitely many solutions. Write answers as integers or fractions in lowest terms.
−8x − 6y = h
12x + ky = 24
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Question 1126889: Find values for h and k so that the system has infinitely many solutions. Write answers as integers or fractions in lowest terms.
−8x − 6y = h
12x + ky = 24
h=
k=
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
both lines should have the same slope and y−intercept
they are one line, coincident, meaning they have all points in common
this means that there are an infinite number of solutions to the system
-------------------
first write both equations in slope-intercept form:
............eq.1=> slope is and y-intercept is
.............eq.2 => slope is and y-intercept is
equal slopes:
...solve for ; both sides multiply by
........cross multiply
equal y-intercepts:
........substitute
......cross multiply
so, your lines are:
->
->
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Since we have linear equations(lines), we want them to have the same slope and y intercept
:
equation 1
:
−8x − 6y = h
:
-6y = 8x +h
:
y = -8x/6 -h/6
:
y = -4x/3 -h/6
:
equation 2
:
12x + ky = 24
:
ky = -12x +24
:
y = -12x/k +24/k
:
the slopes must be equal, therefore
:
-4/3 = -12/k
:
cross multiply the fractions
:
-4k = -36
:
k = 9
:
y intercepts must be equal
:
-h/6 = 24/k
:
we know k = 9
:
-h/6 = 24/9 = 8/3
:
-3h = 48
:
h = -16
:
*******************************************
h = -16 and k = 9
:
check the answer
:
equation 1
:
-8x -6y = -16
:
-4x -3y = -8
:
4x +3y = 8
:
equation 2
:
12x + 9y = 24
:
4x +3y = 8
:
answer checks
********************************************
:
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