Answer:
[tex]x = 15, y = 5[/tex]
Step-by-step explanation:
We are given that
[tex]2x - 4y = 10\\x + 5y = 40[/tex]
When given these types of equations, we can manipulate them in order to cancel out a variable. Cancelling either the x or y works, choose which one is easier.
In this case, we can multiply the second equation by -2 and easily cancel out the x's
[tex]2x - 4y = 10\\-2x - 10y = -80[/tex]
Now we can add the two equations
[tex]-4y + (-10y) = 10 + (-80)\\-4y - 10y = -70\\-14y = -70\\y = 5[/tex]
We can substitute y into the second equation and solve for x
[tex]x + 5(5) = 40\\x + 25 = 40\\ x = 15[/tex]
Check:
2(15) - 4(5)
30 - 20 = 10
it works
