What values of 𝑔g and ℎh make both of these equations true? 𝑔+ℎg+h==14143𝑔−4ℎ3g−4h==−14−14

The equations you provided seem to have some formatting issues. However, I'm assuming you meant the following system of equations:

1. g + h = 14
2. 3g - 4h = -14

To solve this system of equations, you can use the method of substitution or elimination. Here's a step-by-step solution using the elimination method:

Step 1: Multiply the first equation by 3 and the second equation by 1 to make the coefficients of g the same in both equations:

3*(g + h) = 314 1(3g - 4h) = 1*(-14)

This gives us:

3g + 3h = 42 3g - 4h = -14

Step 2: Subtract the second equation from the first:

(3g + 3h) - (3g - 4h) = 42 - (-14)

This simplifies to:

7h = 56

Step 3: Solve for h by dividing both sides of the equation by 7:

h = 56 / 7 h = 8

Step 4: Substitute h = 8 into the first original equation:

g + 8 = 14

Step 5: Solve for g:

g = 14 - 8 g = 6

So, the solution to the system of equations is g = 6 and h = 8.