Supernova
contestada

[tex]10x-16y=12 \\ 5x-3y=4[/tex]


If [tex](x, \ y)[/tex] is a solution to the system of equations above, what is the value of [tex]x-y[/tex] ?

Respuesta :

Space

Answer:

24/25

Step-by-step explanation:

Step 1: Define systems of equation

10x - 16y = 12

5x - 3y = 4

Step 2: Rewrite one of the equations

5x = 4 + 3y

x = 4/5 + 3y/5

Step 3: Solve for y using Substitution

  1. Substitute 2nd rewritten equation into 1: 10(4/5 + 3y/5) - 16y = 12
  2. Distribute the 10 to both terms: 40/5 + 30y/5 - 16y = 12
  3. Simplify the fractions down: 8 + 6y - 16y = 12
  4. Combine like terms (y): 8 - 10y = 12
  5. Subtract 8 on both sides: -10y = 4
  6. Divide both sides by -10: y = 4/-10
  7. Simply the fraction down: y = -2/5

Step 4: Substitute y back into an original equation to solve for x

  1. Substitute: 5x - 3(-2/5) = 4
  2. Multiply: 5x + 6/5 = 4
  3. Subtract 6/5 on both sides: 5x = 14/5
  4. Divide both sides by 5: x = 14/25

Step 5: Check to see if solution set (14/25, -2/5) is a solution.

  1. Substitute into an original equation: 10(14/25) - 16(-2/5) = 12
  2. Multiply each term: 28/5 + 32/5 = 12
  3. Add: 12 = 12

Here, we see that x = 14/25, y = -2/5 and solution (14/25, -2/5) indeed works.

Step 6: Find x - y

x = 14/25

y = -2/5

  1. Substitute: 14/25 - (-2/5)
  2. Simplify (change signs): 14/25 + 2/5
  3. Add: 24/25

Hope this helped! :)

xKelvin

Answer:

[tex]\displaystyle x-y=\frac{24}{25}[/tex]

Step-by-step explanation:

We are given the system:

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

And asked to find the value of x - y if (x, y) is a solution to the above system.

Thus, let's solve the system. We can use eliminiation

We can see that the coefficients of x share a LCM.

Multiplying the second equation by negative two yields:

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

Adding the two equations yields:

[tex](10x-10x)+(-16y+6y)=(12+(-8))[/tex]

Simplify:

[tex]-10y=4[/tex]

Solve for y:

[tex]\displaystyle y = \frac{4}{(-10)} = -\frac{2}{5}[/tex]

To find x, substitute y for either equation and evaluate. The second equation states that:

[tex]5x-3y=4[/tex]

Substitute:

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

Multiply:

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

And solve for x:

[tex]\displaystyle \begin{aligned} 5x+\frac{6}{5} &= 4 \\ \\ 5x &= \frac{14}{5} \\ \\ x &= \frac{14}{25}\end{aligned}[/tex]

Hence, our solution to the system is:

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

We want to find the value of:

[tex]x-y[/tex]

Substitute:

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

Evaluate. Hence:

[tex]\displaystyle x - y = \frac{24}{25}[/tex]

And we're done!

Otras preguntas