In this problem. We have four different songs and were given a set of statements about them to determine the length of each song. So the first statement is that the total playing time off all four songs is 14.3 minutes. So we can write that as w plus X plus y plus z. So the total playing time of each of the four songs is equal to 14.3 minutes are a second statement? Is that, um why song? Why is three minutes shorter than song W So why equals W minus three? Our third statement is that Song Z is 2.7 minutes shorter. Been song X. So soaring Z equals song X minus 2.7 minutes. And then finally, the combined time of Song X and song. Why is five times a song Z? So our fourth statement, the combined Times X Plus y, is equal to five times the length of songs E. And so now we have four equations and we're gonna make it a little simpler by moving all of the unknowns toe one side of the equation. So our first equation remains the same w plus X plus y plus c his 14.3 for a second equation. We're gonna move the w so negative W um, plus y equals negative three for 1/3 equation we're gonna with the X to the other side. So negative x plus Z is equal to negative 2.7. And then for our fourth equation, we're gonna move the sea to the other side. X plus y minus five z is equal to zero. And so now we have it. Now that we have it in this form, we can make it into a matrix. So matrix A is our coefficient matrix. It's gonna be a four by four matrix because we have 1234 equations and w X y and CSR for unknowns in our first equation. All of the coefficients are one for each of the unknowns. In our second equation are coefficient for W is negative. One x There's no X term. So it's zero. Why is one And then there's nosy term, um, for third equation, there's no w or why. But X is negative one and Z is one. And then, for our last equation, there's no w term access. One wise one and these negative five. Then we have our matrix of unknowns, which are W, X, Y and Z, and then finally are matrix of known values on the right side of the equation. So 14.3 negative three negative 2.7 and zero and so to solve for unknowns, we're gonna take her in verse of a and multiply it right B. And so I've already included The Matrix using to a calculator. So we need to do is take the inverse of a and multiply it by B, and we get that song. W is 5.9 minutes. Some X is 4.1, so W's 5.9 x 4.1. Why is 2.9 and see is 1.4. So those are before lengths of thes songs that were unknown.