Question 202288: HI, i cannot seem to find my mistakes in these three questions....can u plzz kindly solve these so i can see where i went wrong?
1) Is the ordered pair (- 2, - 5) a solution to the system of equations defined by 3x - 4y = 14 and 5x + 3y = - 25?
2)Create a linear system of two equations that has no solution.
3)Part of a $5000 prize was invested at 6%, while the remainder was invested at 8%. If the total interest received was $368, how much was invested at each rate?
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1) Is the ordered pair (- 2, - 5) a solution to the system of equations defined by 3x - 4y = 14 and 5x + 3y = - 25?
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If y = -5 when x = -2 you would get:
3*-2 - 4*-5 = 14
-6 + 20 = 14
14 = 14
and
5*-2 - 3*-5 = -25
-10 + 15 = -25
5 = -25
Answer: No
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2)Create a linear system of two equations that has no solution.
y = 2x + 3
y = 2x + 5
These are lines with the same slope and different y-intercepts.
The lines are parallel so there is no solution.
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3)Part of a $5000 prize was invested at 6%, while the remainder was invested at 8%. If the total interest received was $368, how much was invested at each rate?
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interest + interest = interest
0.06x + 0.08(5000-x) = 368
6x + 8(5000-x) = 36800
6x + 40000 - 9x = 36800
-2x = -3200
x = $1600.00 (amt. invested at 6%)
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5000-x = 5000-3200 = $1800 (amt. invested at 8%)
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Cheers,
Stan H.
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website! 1) To see if the ordered pair (-2, -5) is a solution to the given system of equations, you can do it algebraically or graphically.
Algebraically:
Substitute the ordered pair (-2, -5) into both equations:
3x-4y = 14
3(-2)-4(-5) = 14
-6+20 = 14
14 = 14 OK!
5x+3y = -25
5(-2)+3(-5) = -25
-10+(-15) = -25
-25 = -25 OK!
The answer is yes!
Graphically:
The point of intersection (-2, -5) of the two lines is the solution to the system of equations.
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2) Here, all you need to do is to write two linear equations the have the same slope (parallel lines) but different y-intercepts.
Use the slope-intercept form (y = mx+b) for convenience.
a) y = 3x+4
b) y = 3x+8
There is no solution because the parallel lines do not intersect and it is the point of intersection that is the solution to a system of linear equation. See the graph below:
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3) Let x = the amount invested at 6%, then ($5000-x) is the amount invested at 8%.
The interest earned on these two amounts ($368) can be expressed as:
6%(x)+8%($5000-x) = $368 Simplify and solve for x. Change the percentages to their decimal equivalents.
0.06(x)+0.08(5000-x) = 368 Simplify and solve for x.
0.06x+400-0.08x = 368 Combine the x-terms on the left.
-0.02x+400 = 368 Subtract 400 from both sides.
-0.02x = -32 Finally, divide both sides by -0.02
x = $1600 and 5000-x = $3400
$1600.00 was invested at 6% and $3400.00 was invested at 8%.
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