Solve the system by either substitution or elimination. Show your work to prove your answer
3x – 5y = 21
2x + y = 1
To solve this system by elimination, we will multiply the second equation by -5 to make the coefficients of y add up to 0:
(-5)(2x + y) = (-5)(1)
-10x - 5y = -5
Now, we can add the two equations together:
(3x – 5y) + (-10x - 5y) = 21 + (-5)
-7x - 10y = 16
Simplifying the left side by combining like terms, we get:
-7x - 10y = 16
To solve this system by substitution, we can solve the second equation for y:
2x + y = 1
y = 1 - 2x
Now, we can substitute this expression for y into the first equation:
3x - 5(1 - 2x) = 21
3x - 5 + 10x = 21
13x - 5 = 21
13x = 26
x = 2
Now that we have a value for x, we can substitute it back into the second equation to find y:
2(2) + y = 1
4 + y = 1
y = 1 - 4
y = -3
Therefore, the solution to the system of equations is x = 2 and y = -3.