In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0, b ≠ 0 5ax + 4y = 17 ax + 7y = 22

Question

Exercise 49: Two equations for solving x and y in terms of a and b.

Accepted Answer

Welcome back. I am so glad you're here. We are given two equations in our system of equations. The first equation is two. A X minus three Y equals 12. And the second equation is a X plus six Y equals 18. And we are to solve for X and Y recalling previous lessons on systems of equations and solving. I am going to use the addition method for solving for Y. So I'm going to get our X terms to cancel out. I'm going to do that by taking the second equation and multiplying it by negative two and then adding that to the first equation. So a X times negative two is negative two. X six, Y times negative two is minus 12. Y equals 18 times negative two is negative 36. Now adding equations one and blue, we'll get the X terms cancel out negative three Y plus negative 12 Y is negative 15, Y equals 12 plus A negative 36 is negative 24 dividing both sides by negative 15 to get y by itself and negative 24 negative 15th. While the negatives cancel out. So that's 24 15th and 15 are both divisible by three. So we will get a Y equals 24 divided by three is 8, 15 divided by three is five. So y equals 8/5. Now we can take that 8/5 and substitute that in for Y. So that we can solve for X. I'm going to use the second equation here and substitute 8/5 and for the Y in the second equation. So rewriting that will have A. X plus six times no longer Y. But now six times 8/5 equals 18. Well six times 8/5 is plus 48 5th equals 18. And now subtracting 48 5th. So from both sides and on the left hand side they cancel out. So the left hand side is A. X. And equals 18 minus 48 5th is 42 5th. And now we just have that A. So we can divide both sides by Excuse me, I wanted to switch colors, divide both sides by A. And then the a. Goes into the denominator on the right hand side. So we get x equals 42 divided by five a. And we have solved for X and Y. We look at our answer choices and this matches with answer choice B. Well done. We'll catch you on the next one.

In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0, b ≠ 0 5ax + 4y = 17 ax + 7y = 22

Verified Solution