Final answer:
To solve the given system of equations x-3y=-13 and 3x+7y=25 using elimination, the first equation is multiplied by 3 to align the y terms, and then the equations are subtracted from each other to solve for y, followed by substituting y's value to solve for x. The solution is x = -1, y = 4.
Step-by-step explanation:
To solve the system of equations {x-3y=-13, 3x+7y=25} using elimination, you first need to align the equations so that either the x's or the y's can easily be eliminated. Let's multiply the first equation by 3.
3(x - 3y) = 3(-13)
3x - 9y = -39
Now, let's subtract the new first equation from the second equation:
(3x + 7y) - (3x - 9y) = (25 - (-39))
16y = 64
Solving for y gives:
y = 64 / 16
y = 4
Now substitute y back into one of the original equations to find x:
x - 3(4) = -13
x - 12 = -13
x = -13 + 12
x = -1
The solution to the system of equations is thus x = -1, y = 4.