Question 202288
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:
{{{graph(400,400,-5,5,-10,5,(3/4)x-7/2,(-5/3)x-25/3)}}}
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:
{{{graph(400,400,-5,5,-5,5,3x+4,3x+8)}}}
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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%.