Solve the system by the addition method. −5x+7y=4
4x−y=−17
28x - 7y = -119 ... add to 1st eqn
To solve the system of equations using the addition method, we need to add the two equations together in such a way that either the x or y terms will cancel out.
Let's start by multiplying the second equation by 7 to make the y term of both equations have the same coefficient (both 7y):
7(4x - y) = 7(-17)
28x - 7y = -119
Now we can add the modified second equation to the first equation:
-5x + 7y + (28x - 7y) = 4 + (-119)
Combining like terms:
-5x + 28x + 7y - 7y = -115
Simplifying:
23x = -115
Next, we divide both sides of the equation by 23 to solve for x:
x = -115/23
x = -5
Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
-5(-5) + 7y = 4
Simplifying:
25 + 7y = 4
Subtracting 25 from both sides:
7y = 4 - 25
7y = -21
Finally, we divide both sides by 7 to solve for y:
y = -21/7
y = -3
Therefore, the solution to the system of equations is x = -5 and y = -3.