Solve the system using elimination.
x+3y=7
7x-3x=1
The solution is
(Simplify your answer. Type an ordered pair.)
The given system of equations is:
1) x + 3y = 7
2) 7x - 3x = 1
To solve this system using elimination, we want to eliminate one variable by multiplying one or both equations by appropriate constants so that when we add or subtract them, one variable will cancel out.
Let's multiply equation 1 by -3 and equation 2 by 3:
-3(x + 3y) = -3(7)
3(7x - 3y) = 3(1)
Simplifying:
-3x - 9y = -21
21x - 9y = 3
Now we can add the two equations to eliminate y:
(-3x - 9y) + (21x - 9y) = -21 + 3
-3x + 21x - 9y - 9y = -18
18x - 18y = -18
Divide all terms by 18 to solve for x:
x - y = -1
Now, we can substitute this value of x into equation 1 to solve for y:
(-1) + 3y = 7
3y = 8
y = 8/3
Therefore, the solution to the system is (x, y) = (-1, 8/3).