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if x-y=80 and 3/5=y/x <--(as a fraction), what is the value of x? will give 45 points, and brainliest for the right answer

Sagot :

mhanifa

Answer:

  • (200, 120)

Step-by-step explanation:

Given system

  • x - y = 80
  • 3/5 = y/x

Solve it by substitution

  • y = 3/5(x)
  • y = x - 80

Find the value of x

  • 3/5(x) = x - 80
  • x - 3/5(x) = 80
  • 2/5(x) = 80
  • x = 80*5/2
  • x = 200

Find the value of y

  • y = 3/5(200)
  • y = 120
semsee45

Answer:

x = 200

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}x-y=80\\\\\dfrac{3}{5}=\dfrac{y}{x} \end{cases}[/tex]

Rearrange the second equation to make y the subject by multiplying both sides by x:

[tex]\implies \dfrac{3}{5} \cdot x=\dfrac{y}{x} \cdot x[/tex]

[tex]\implies y=\dfrac{3}{5}x[/tex]

Substitute this into the first equation and solve for x:

[tex]\implies x-\left(\dfrac{3}{5}x\right)=80[/tex]

[tex]\implies \dfrac{2}{5}x=80[/tex]

[tex]\implies \dfrac{2}{5}x \cdot 5=80 \cdot 5[/tex]

[tex]\implies 2x=400[/tex]

[tex]\implies \dfrac{2x}{2}=\dfrac{400}{2}[/tex]

[tex]\implies x=200[/tex]

Therefore, the value of x is 200.

If you want to find the value of y, simply substitute the found value of x into the first equation and solve for y:

[tex]\implies 200-y=80[/tex]

[tex]\implies 200-y+y=80+y[/tex]

[tex]\implies 200=y+80[/tex]

[tex]\implies 200-80=y+80-80[/tex]

[tex]\implies 120=y[/tex]

[tex]\implies y=120[/tex]

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