Question

Hi can you translate this for me using numbers please? Thank you so much!

Answer 1

Here it is:

This is Mrs. Simmons, and we will solve the system three x plus two y equals thirty and six x plus two y equals three times the quantity three y plus nine using the linear combination method. In order to know which variables eliminate, we need to write the second equation in standard form. So we take that equation, six x plus two y equals three times the quantity three y plus nine, and we distribute the three on the right side of the equation to get nine y plus twenty-seven. Then, we need to collect all the y-terms to
one side, so we subtract nine y from both sides in order to get six x minus seven y equals twenty-seven. Our next step will be to actually eliminate a variable. Let’s compare our two equations in order to decide which variable to eliminate. We’ve got three x and six x, which have a common factor of three, and two y and negative seven y, which don’t have any common factors. So let’s choose to eliminate the x’s. The least common multiple of three and six is six. So we’ll need to multiply that first equation
through by a negative two in order to have a negative six to eliminate this positive six x. So we distribute through by the negative two to get negative six x minus four y equals negative sixty. Next, we will add our two simplified equations together in order to try to eliminate the x values. So we’ve got negative six x minus four y equals negative sixty and six x minus seven y equals twenty-seven. Negative six x plus six x is zero. Negative
four y minus seven y is negative eleven y, and negative sixty plus twenty seven is negative thirty-three. Then, we divide both sides by negative eleven in order to get y equals three. We are halfway there because we have one of the coordinates. So our next step will be to substitute for y in either equation in order to find x. Let’s go ahead and use that first equation since it’s the most simplified. So we plug in three for y into
the second equation to get three x plus two times three equals thirty. Two times three is six, so we have three x plus six equals thirty. We subtract six from both sides to get
three x equals twenty-four, and then divide both sides by three in order to get x equals eight. Our last step will be to write the solution as an ordered pair. So our solution x equals eight and y equals three becomes the point eight comma three, and we have a solution to our system.