Answer:
[tex]x=2[/tex] and [tex]y=8[/tex]
Step-by-step explanation:
Given:
Equation 1:
[tex]500y-600x=2800[/tex]
Simplifying the above equation by dividing both sides by 100
[tex]\frac{500y-600x}{100}=\frac{2800}{100}[/tex]
[tex]\frac{500y}{100}-\frac{600x}{100}=28\\\\5y-6x=28[/tex]
Equation 2:
[tex]400y-400x=2400[/tex]
Simplifying the above equation by dividing both sides by 400.
[tex]\frac{400y-400x}{400}=\frac{2400}{400}[/tex]
[tex]\frac{400y}{400}-\frac{400x}{400}=6\\\\y-x=6[/tex]
Now the system of equation is:
(1a) [tex]5y-6x=28[/tex]
(2a) [tex]y-x=6[/tex]
Solving by elimination
Multiplying equation (2a) with [tex]-5[/tex]
[tex]-5(y-x)=-5\times 6[/tex]
(2b) [tex]-5y+5x=-30[/tex]
Adding equations (1a) and (2b) in order to eliminate [tex]y[/tex]
[tex]5y-6x=28[/tex]
+ [tex]-5y+5x=-30[/tex]
We get [tex]-x=-2[/tex]
∴ [tex]x=2[/tex]
Plugging [tex]x=2[/tex] in equation (2a).
[tex]y-2=6[/tex]
Adding [tex]2[/tex] both sides.
[tex]y-2+2=6+2[/tex]
∴ [tex]y=8[/tex]
