What is the y-coordinate of the solution of the system of equations?
y=2x+14
−4x−y=4
Enter your answer in the box.
y = ?
The answer is 8
well, you know that 2x = y-14
So, use that in the other equation:
-4x = -2(2x), so
-2(y-14)-y = 14
...
To find the y-coordinate of the solution of the system of equations, we need to find the values of x and y that satisfy both equations simultaneously.
Let's solve the system by the method of substitution:
1. Start with the first equation: y = 2x + 14.
2. Substitute this expression for y in the second equation: -4x - (2x + 14) = 4.
3. Simplify the equation: -4x - 2x - 14 = 4.
4. Combine like terms: -6x - 14 = 4.
5. Add 14 to both sides of the equation: -6x = 18.
6. Divide both sides by -6: x = -3.
Now that we have the value of x, we can substitute it back into either equation to find the corresponding y-coordinate.
Let's substitute x = -3 into the first equation: y = 2(-3) + 14 = -6 + 14 = 8.
Therefore, the solution to the system of equations is x = -3 and y = 8.
So the y-coordinate of the solution is 8.