what is the value of the y-coordinate of the solution to the system of equations: x-2y=1 and x+4y=7
1) 1
2) -1
3) 3
4) 4
-6y = -6
y = 1
To find the value of the y-coordinate of the solution to the system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
1. Solve one of the equations for one variable (in terms of the other variable). Let's solve the first equation for x:
x = 2y + 1
2. Substitute this expression for x in the second equation:
(2y + 1) + 4y = 7
3. Simplify the equation:
2y + 1 + 4y = 7
6y + 1 = 7
6y = 6
y = 1
4. The value of y is 1.
Therefore, the correct answer is option 1) 1.
Method 2: Elimination
1. Multiply the first equation by 4 and the second equation by -2 so that the coefficients of y will cancel each other out:
4(x - 2y) = 4(1)
-2(x + 4y) = -2(7)
4x - 8y = 4
-2x - 8y = -14
2. Add the two equations together:
(4x - 8y) + (-2x - 8y) = 4 + (-14)
4x - 2x - 8y - 8y = 4 - 14
2x - 16y = -10
3. Divide both sides of the equation by 2 to simplify:
x - 8y = -5
4. Solve this equation for x in terms of y:
x = 8y - 5
5. Substitute this expression for x in the first equation:
(8y - 5) - 2y = 1
6. Simplify the equation:
8y - 5 - 2y = 1
6y - 5 = 1
6y = 6
y = 1
7. The value of y is 1.
Again, the correct answer is option 1) 1.