Question

Can you please help me solve 18 and 21 please?

Answer 1

Answer:

18. x = y = -3

21. y was substituted into the wrong equation. The solution is (x, y) = (2, 1).

Step-by-step explanation:

18. Adding y to the first equation transforms it to ...

... x = y

Then you can substitute for either variable in the second equation.

... 2y -5y = 9 . . . . . substitute for x

... -3y = 9 . . . . . . . . simplify

... y = -3 . . . . . . . . . divide by the coefficient of y

.. x = -3 . . . . . . . . . x and y have the same value

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21. The first equation is being used to find an expression for y in terms of x. If you substitute that expression back into the same equation, it will tell you nothing you didn't already know. (Here, it is telling you 5 = 5.) The expression is only useful if you substitute it into a different equation. Here, it needs to be substituted into the second equation:

... Step 2: 3x -2(-2x+5) = 4 ⇒ 7x -10 = 4 . . . . . substitute for y in the second eqn

... Step 3: 7x = 14 . . . . . add 10

... Step 4: x = 2 . . . . . . . divide by 7

... Step 5: y = -2·2 +5 = 1 . . . . . find the value of y from x using the expression from step 1. Now, you know the solution is (x, y) = (2, 1).

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The attached graph shows the solution to the problem of 21.