In Exercises 71–74, determine whether each statement is true or f...

Question

In Exercises 71–74, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The ordered pair (2, 5) satisfies 3y - 2x = - 4.

Accepted Answer

Welcome back. I'm so glad you're here. Were given an ordered pair 13 and told it satisfies the equation. Nine Y minus seven X equals negative 12. And if maybe that doesn't happen to be true then we need to figure out what ordered pair would make it true. So let's see if that ordered pair works. We need to recall first from previous lessons that an ordered pair gives us an X. Value followed by a Y. Value. So therefore wherever we see an X. In our equation we can plug in that X. Value or in this case of one and whenever we see a Y. In our equation we can plug in that Y value in this case A. Three. So we can rewrite this instead of nine Y. We've got nine times three minus instead of seven X. We've got seven times one equals negative 12. Let's simplify nine times three is 27 minus seven times one is seven so 27 minus seven equals negative 12. No it doesn't that's 20 and that doesn't equal negative 12. Therefore the statement is not true. Let's see if any of these other ordered pairs work. So again it's X. First and then y let's test this second one. So we've got nine times our new y values three and minus seven times our new X value is negative one equals negative 12. 9 times three. That's 27. Still negative seven times negative one. Well that's going to be a plus seven equals negative 12. No that's way too big. That one is not going to work. So it's not going to be be either. Let's give C a try, we'll try one negative three. So nine times our new y value is going to be negative three -7 times. Our new x value is one equals negative 12. So nine times negative three is negative 27. Hey we're in the negatives now minus seven times one is minus seven. No that's just going to get us more negative beyond negative 27. So no it is not going to be answer choice C. So let's see if the works. We've got nine times our new Y value is one minus seven times our new X values. Three equals negative 12. So that's nine times one is nine minus seven times three is 21. And hey look that does equal negative 12. So we have found our correct ordered pair that leaves us with answer choice. D Well done. We'll catch you on the next one.

In Exercises 71–74, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The ordered pair (2, 5) satisfies 3y - 2x = - 4.

Key Concepts

Ordered Pairs

Substitution in Equations

Linear Equations

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