What values of 𝑔g and ℎh make both of these equations true? 𝑔+ℎg+h==13134𝑔−5ℎ4g−5h==−29−29

The equations you provided are:

1. g + h = 13
2. 4g - 5h = -29

This is a system of linear equations. We can solve it step by step:

Step 1: Multiply the first equation by 4 and the second equation by 1 to make the coefficients of g the same in both equations:

4g + 4h = 52 4g - 5h = -29

Step 2: Subtract the second equation from the first to eliminate g:

4h + 5h = 52 + 29 9h = 81 h = 81 / 9 h = 9

Step 3: Substitute h = 9 into the first equation to find g:

g + 9 = 13 g = 13 - 9 g = 4

So, the values of g and h that make both of these equations true are g = 4 and h = 9.