what is the value of the y-coordinate of the solution to the system of equations x-2y=1 and x+4y=7
subtract the first equation from the second to get
6y = 6
y = 1
To find the value of the y-coordinate of the solution to the given system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:
Step 1: Multiply the first equation by 4 and the second equation by 2 to make the coefficients of y in both equations equal:
4(x-2y) = 4(1)
2(x+4y) = 2(7)
Simplifying these equations gives us:
4x - 8y = 4
2x + 8y = 14
Step 2: Add the two equations together to eliminate the variable y:
(4x - 8y) + (2x + 8y) = 4 + 14
6x = 18
Step 3: Divide both sides of the equation by 6 to solve for x:
6x/6 = 18/6
x = 3
Step 4: Substitute the value of x into either of the original equations. Let's use the first equation:
3 - 2y = 1
Step 5: Solve this equation for y:
-2y = 1 - 3
-2y = -2
y = -2/-2
y = 1
Therefore, the value of the y-coordinate of the solution to the given system of equations is y = 1.
To find the value of the y-coordinate of the solution to the system of equations x-2y=1 and x+4y=7, we can use the method of substitution.
First, let's solve one of the equations for x in terms of y. We choose the first equation, x-2y=1.
Step 1: Add 2y to both sides of the equation:
x = 2y + 1
Now we can substitute this expression for x in the second equation, x+4y=7:
(2y + 1) + 4y = 7
Step 2: Combine like terms:
6y + 1 = 7
Step 3: Subtract 1 from both sides of the equation:
6y = 6
Step 4: Divide both sides of the equation by 6:
y = 1
Therefore, the value of the y-coordinate of the solution to the system of equations is 1.