solve the following system by the elimination method 5x+y=-19
7x-3y=-53
To solve the system of equations by the elimination method, we need to eliminate one variable by multiplying one or both equations by a suitable number(s) so that the coefficients of one of the variables in both equations have the same magnitude but opposite signs.
We can start by multiplying the first equation by 3 and the second equation by 1, so the coefficients of "y" will have the same magnitude but opposite signs.
3 * (5x + y = -19) gives us:
15x + 3y = -57
1 * (7x - 3y = -53) gives us:
7x - 3y = -53
Now, if we add the two equations together, the "y" terms will cancel out:
(15x + 3y) + (7x - 3y) = -57 + (-53)
15x + 7x + 3y - 3y = -57 - 53
22x + 0 = -110
Simplifying further:
22x = -110
To solve for "x," divide both sides of the equation by 22:
22x/22 = -110/22
x = -5
Now, substitute the value of "x" back into one of the original equations, for example, using the first equation:
5x + y = -19
5(-5) + y = -19
-25 + y = -19
To solve for "y," add 25 to both sides of the equation:
-25 + 25 + y = -19 + 25
y = 6
Therefore, the solution to the system of equations is x = -5 and y = 6.