How do you solve the system of equations #x- y = 7# and #- 2x + 5y = - 8#?
By manipulating the first equation and combining it with the second, we can eventually arrive at the answer: x = 9, y = 2.
Your goal here is to remove one of the variables from the problem. You can see that the first equation has x and the second equation has -2x. If we double the first equation, we get:
Then we simply add that to the second equation:
The positive 2x and the negative 2x cancel out, leaving us with just the 3y = 6.
Divide both sides by 3 and we get y=2.
Last, just plug 2 in for y in either equation (I'll choose the first since it's simpler):
Add 2 to both sides to get x=9.
So our final answer is x = 9, y = 2.
You will need to solve one of the variables using the substitution method.
Begin by solving either the
To Solve for
Now plug in the
We have now solved both variables. Check to make sure both equations are equal.
The point of intersection between the two lines is
Refer to the explanation for the process.
Solve system of equations:
These are linear equations. Since they are a system, both equations are solved simultaneously by substitution. The resulting values for x and y is the point at which the two lines intersect on a graph.
The two equations are:
Divide both sides by
Now substitute the value of
The point of intersection is