Question

$\begin{gathered}10x-16y=12 \\ 5x-3y=4\end{gathered}$


If (x, y) is a solution to the system of equations above, what is the value of x-y?​

Answer 1

$\huge{\underline{\underline{\mathcal\color{gold}{\bigstar{Answer\bigstar }}}}}$

$\red{x-y=\dfrac{24}{25}}$

Step-by-step explanation:

$\rightsquigarrow$ We have the system:

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

$\rightsquigarrow$ We can solve this system by elimination.

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

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

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

$\rightsquigarrow$ Multiply:

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

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

$\bold{(10x-10x)+(-16y+6y)=(12+(-8))}$

Add:

$\tt{-10y=4   }$      

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

$\bold{y=\dfrac{4}{-10}=\dfrac{-2}{5 }  }$ 

$\rightsquigarrow$ We can substitute this back into either equation to find x.

Let's use the second equation:

$\tt{ 5x-3y=4  }$      

$\rightsquigarrow$ Substitute -2/5 for y:

$5x-3(-\dfrac{2}{5})=4$

$\rightsquigarrow$ Multiply:

$5x+\dfrac{6}{5}=4$

$\rightsquigarrow$ Subtract 6/5 from both sides. Note that 4 is the same as 20/5.

$\rightsquigarrow$ So:

$5x=\dfrac{20}{5}-\dfrac{6}{5}$

$\rightsquigarrow$ Subtract:

$5x=\dfrac{14}{5}$

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

$x=\frac{14}{25}$

$\rightsquigarrow$ Therefore, our solution is:

$(\dfrac{14}{25},- \dfrac{2}{5})$

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

$\rightsquigarrow$ We want to find:

x-y

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

$=\dfrac{14}{25}-(-\dfrac{2}{5})$

$\rightsquigarrow$ Simplify. Change 2/5 to 10/25:

$=\dfrac{14}{25}+\dfrac{10}{25}$

$\hookrightarrow$ Add. So, our answer is:

$=\dfrac{24}{25}$

Answer 2

Answer:

The value of x - y = 24/25

Step-by-step explanation:

Given:

Equation I: 10x - 16y = 12

Equation II: 5x - 3y = 4

Divide 2 with equation I:

10x/2 - 16y/2 = 12/2

→ 5x - 8y = 6

Now subtract equation I from equation II:

5x - 3y - (5x - 8y) = 4 - 6

→ 5x - 3y - 5x + 8y = - 2

→ 5y = - 2

→ y = - 2/5

Now substitute the value of y in equation II:

5x - 3(-2/5) = 4

→ 5x + 6/5 = 4

→ 5x = 4 - 6/5

→ 5x = (20 - 6)/5

→ 5x = 14/5

→ x = 14/25

Value of x - y:

= 14/25 - (-2/5)

= 14/25 + 2/5

= (14 + 10)/25

= 24/25