Solving Quadratic System
y=4x+1
2x-y+1
Please show work!!!
You can solve this problem the same way I showed you for the last problem.
is the correct answer is x=-1 and y=-3
you can easily check by substituting in those values to see whether they work in both equations.
FYI, they do.
thank you
To solve the quadratic system, we need to find the values of x and y that satisfy both equations simultaneously.
The given equations are:
1) y = 4x + 1
2) 2x - y + 1 = 0
To solve this system, we can use the method of substitution or the method of elimination. Let's use the method of substitution:
Step 1: Solve one equation for one variable in terms of the other variable. From equation (1), we can express y in terms of x: y = 4x + 1.
Step 2: Substitute the expression for y in equation (2) with the equivalent expression from step 1:
2x - (4x + 1) + 1 = 0
Simplifying the equation:
2x - 4x - 1 + 1 = 0
-2x = 0
x = 0
Step 3: Substitute the value of x back into one of the original equations to find the corresponding value of y. We'll use equation (1):
y = 4(0) + 1
y = 1
So, the solution to the quadratic system is x = 0 and y = 1.
To check the solution, substitute the values of x and y back into both equations:
1) Equating with equation (1):
1 = 4(0) + 1
1 = 1 (true)
2) Equating with equation (2):
2(0) - 1 + 1 = 0
0 = 0 (true)
Both equations are satisfied, confirming that x = 0 and y = 1 is indeed the solution to the quadratic system.