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Answer:
Step-by-step explanation:
Given system
Solve it by substitution
Find the value of x
Find the value of y
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]