Solve the system x+4y=1,-x+y=4.What is the -coordinate of this solution
x.
To solve the given system of equations:
1. Start by labeling the equations as Equation 1 and Equation 2 for easy reference.
Equation 1: x + 4y = 1
Equation 2: -x + y = 4
2. Choose a method to solve the system. In this case, we will use the method of substitution.
3. Solve Equation 2 for one variable in terms of the other. Let's solve Equation 2 for x:
-x + y = 4
Adding x to both sides: -x + x + y = 4 + x
Simplifying: y = x + 4
4. Substitute the expression for y from Step 3 into Equation 1:
x + 4y = 1
x + 4(x + 4) = 1
x + 4x + 16 = 1
Combining like terms: 5x + 16 = 1
Subtracting 16 from both sides: 5x = 1 - 16
Simplifying: 5x = -15
Dividing both sides by 5: x = -3
5. The value of x in this system is -3. Therefore, the x-coordinate of the solution is -3.
You know from eq #2 that y=x+4. So, plug that into eq #1 and you have
x + 4(x+4) = 1
Now you can find x.