In Exercises 61–66, find all values of x satisfying the given ...

Question

In Exercises 61–66, find all values of x satisfying the given conditions. $y_1 = \frac{x - 3}{5}, \quad y_2 = \frac{x - 5}{4}, \quad ext{and} \quad y_1 - y_2 = 1$

Accepted Answer

Welcome back. I'm so glad you're here. We are to find A and we're given three different equations here in order to figure it out. Our first one, we've got Y sub one equals a minus 2/7. We've got Y sub two equals a minus 13/11. And then we've got y sub one minus Y sub two equals five. Well this is nice because that third equation uses both the Y sub one and Y sub two. So we can actually just go through And we can use substitution so we can substitute in for why someone in the third equation, we can substitute a -2 over seven. And for this third equation for the Y sub two, we can just go back and substitute a minus 13 over 11 And that all equals five. Well now we can just go ahead and solve for a let's get rid of the fraction first. What's our common denominator? While the common denominator of seven and 11 is going to be 77. So now we're going to take our first one here A -2-7 and we're going to multiply that by And subtracting our a -13 divided by 11. And now that numerator is times And that equals five times 77. Now the fun part, when we're clearing fractions, we go back and we look and we say, oh look this 77 divided by seven, that's just going to give us 11 in the numerator. And this 77 divided by 11, that's just going to give us seven in the numerator. So now we've got 11 times a minus two -7 times a -13 equals and five times 77 is 385. Now we can go ahead and do our distribution. Take that 11 and distributed and the negative seven and distributed to get rid of our parentheses. So 11 times A. Is 11 a minus two times 11 is negative seven times a is minus seven A negative seven times negative 13 is positive 91 that equals 385. Now let's see what our like terms are. We've got an 11 A. And a minus seven A. And we've got a negative 22 a plus 91. So the 11 a minus seven A. That gives us four a negative 22 plus 91 gives us plus 69 which equals 385. Now we can subtract 69 from both sides trying to get that a by itself And we've got four a equals because positive 69 -69 cancels out four a equals 385 -69 is 316. We've almost got a by itself. Now we are just going to say the four is being multiplied by the ace. We've got to undo that with division divide both sides by four on the left hand side. The forest cancel out and become a one. So that's just one A or a equals divided by four is 79. That is as simplified as it's going to get. We look at our answer choices and that matches with answer choice. A well done, we'll catch you on the next one.

In Exercises 61–66, find all values of x satisfying the given conditions. $y_1 = \frac{x - 3}{5}, \quad y_2 = \frac{x - 5}{4}, \quad \text{and} \quad y_1 - y_2 = 1$

Key Concepts

Solving Linear Equations

Substitution Method

Understanding Linear Functions

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