SOLUTION: The system of equations below has multiple solutions, all of which satisfy the equation y=4/3x-2. What is the value of a?
8x-6y=12
12x-ay=18
a. -6
b. 9
c. 14
d. 18
Algebra.Com
Question 987529: The system of equations below has multiple solutions, all of which satisfy the equation y=4/3x-2. What is the value of a?
8x-6y=12
12x-ay=18
a. -6
b. 9
c. 14
d. 18
Found 2 solutions by algebrahouse.com, MathLover1:
Answer by algebrahouse.com(1659) (Show Source): You can put this solution on YOUR website!
Since they have multiple solutions, they should all look the same when put into slope-intercept form.
y = (4/3)x - 2 {first equation is already in slope-intercept form}
8x - 6y = 12 {second equation}
-6y = -8x + 12 {subtracted 8x from each side}
y = (4/3)x - 2 {divided each side by -6, getting into slope-intercept form}
Notice the second equation is now the same as the first, when put into slope-intercept form.
12x - ay = 18 {third equation}
-ay = -12x + 18 {subtracted 12x from each side}
y = (12/a)x + (-18/a) {divided each side by -a}
The question, now, is what number would make the 12/a into 4/3 and the -18/a into -2?
9 would
b.) 9
For more help from me, visit: www.algebrahouse.com
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
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this will be equal if:
=>
=>
so, your answer is:
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