[tex]\begin{gathered}10x-16y=12 \\ 5x-3y=4\end{gathered}[/tex]
If (x , y) is a solution to the system of equations above, wha

2 thoughts on “[tex]\begin{gathered}10x-16y=12 \\ 5x-3y=4\end{gathered}[/tex]<br />If (x , y) is a solution to the system of equations above, wha”

1. Answer:

   [tex]Assuming 15 is the length of the “roof” of the trapezoid and 23 is the length of the entire base of the trapezoid:

   ANSWER

   171 square units

   EXPLANATION

   The area of a trapezoid is given by

   Area = 1/2(a+b)(h)

   where a and b are the lengths of the “roof” and the base (order of addition does not matter) and h is the height of the trapezoid.

   Therefore,

   Area = 1/2(15 + 23)(9) = 171

   The area of this trapezoid is 171 square units.[/tex]

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2. Answer:

   We have the system:

   [tex]\begin{gathered}\left\{ \begin{array}{ll} 10x-16y=12 & \quad \\ 5x-3y=4& \quad \end{array} \right.\end{gathered}[/tex]

   We can solve this system by elimination.

   Looking at the system, we can see that the coefficients of the Xs share a LCM.

   So, we can multiply the second equation by -2. This yields:

   [tex]\begin{gathered}\left\{ \begin{array}{ll} 10x-16y=12 & \quad \\ -2(5x-3y)=-2(4)& \quad \end{array} \right.\end{gathered}[/tex]

   Multiply:

   [tex]\begin{gathered}\left\{ \begin{array}{ll} 10x-16y=12 & \quad \\ -10x+6y=-8 & \quad \end{array} \right.\end{gathered}[/tex]

   Now, we can add the two equations. This yields:

   (10x-10x)+(-16y+6y)=(12+(-8))

   Add:

   -10y = 4

   Divide both sides by -12. So, the value of y is:

   y = 4/-10 = -2/5

   We can substitute this back into either equation to find x. Let’s use the second equation:

   5x-3y = 4

   Substitute -2/5 for y:

   [tex]5x-3(-\frac{2}{5})=4[/tex]

   Multiply:

   [tex]5x+\frac{6}{5}=4[/tex]

   Subtract 6/5 from both sides. Note that 4 is the same as 20/5. So:

   [tex]5x=\frac{20}{5}-\frac{6}{5}[/tex]

   Subtract:

   [tex]5x=\frac{14}{5}[/tex]

   Multiply both sides by 1/5. So, the value of x is:

   [tex]x=\frac{14}{25}[/tex]

   Therefore, our solution is:

   [tex](\frac{14}{25},- \frac{2}{5})[/tex]

   Where x is 14/25 and y is -2/5.

   We want to find:

   x – y

   Substitute 14/25 for x and -2/5 for y:

   [tex]=\frac{14}{25}-(-\frac{2}{5})[/tex]

   Simplify. Change 2/5 to 10/25:

   [tex]=\frac{14}{25}+\frac{10}{25}[/tex]

   Add. So, our answer is:

   [tex]=\frac{24}{25}[/tex]

   And we’re done!

   Best of luck for your exam!

   Reply