Solve using elimination.
3x + 3y = –15
–3x − 4y = 14
Add both equations to solve for y, then insert the y value into one of the equations to find x.
To solve the system of equations using elimination, we need to eliminate one variable by adding or subtracting the equations.
Looking at the given equations:
1) 3x + 3y = -15
2) -3x - 4y = 14
We can see that the coefficients of the variable "x" in both equations are opposites of each other. Thus, if we add these two equations, the x-term will be eliminated.
Adding the equations (1) and (2):
(3x + 3y) + (-3x - 4y) = -15 + 14
3x - 3x + 3y - 4y = -1
-y = -1
Now, we have a simplified equation with only one variable. To solve for "y", we can multiply both sides of the equation by -1 to isolate "y":
-y * (-1) = -1 * (-1)
y = 1
Next, substitute the value of "y" back into one of the original equations. Let's use equation (1):
3x + 3(1) = -15
3x + 3 = -15
3x = -15 - 3
3x = -18
Finally, solve for "x" by dividing both sides by 3:
3x/3 = -18/3
x = -6
Therefore, the solution to the system of equations is x = -6 and y = 1.