Solve the following systems of equations:
-2x+y=1
-4x+y=-1
(3,1)
(-1,3)
(-1,-3)
(1,3)
Could someone please help. I'm confused on how to solve this. Thank you!
-2x+y=1
-4x+y=-1
------------ subtract because coefficient of y is the same
-2x + 4x + 0 = 1+1 = 2
2 x = 2
x = 1
then
-2(1) + y = 1
y = 3
so in the end
(1,3)
There are a couple of ways to solve this. However, I worked backwards, plugging the numbers in your answer choices into the original equations.
This is what I found.
1, 3
okay thank you. I understand it better now.
To solve a system of equations, you can use the method of substitution or elimination. Let's solve this system using the elimination method:
Given system of equations:
-2x + y = 1 ........(Equation 1)
-4x + y = -1 .......(Equation 2)
Step 1: Multiply Equation 1 by -1
-1(-2x + y) = -1(1)
2x - y = -1 .......(Equation 3)
Step 2: Subtract Equation 3 from Equation 2
(-4x + y) - (2x - y) = -1 - (-1)
-4x + y - 2x + y = -1 + 1
-6x = 0
Divide both sides of the equation by -6:
-6x / -6 = 0 / -6
x = 0
Step 3: Substitute the value of x (which is 0) into Equation 1 or 2 to solve for y. I'll use Equation 1:
-2(0) + y = 1
0 + y = 1
y = 1
So, the solution to the system of equations is x = 0 and y = 1. Therefore, the correct solution is (0, 1).