18. x = y = -3
21. y was substituted into the wrong equation. The solution is (x, y) = (2, 1).
<h3>Step-by-step explanation:</h3>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 <em>substitute it into a different equation</em>. Here, it needs to be substituted into the second equation:
... <u>Step 2</u>: 3x -2(-2x+5) = 4 ⇒ 7x -10 = 4 . . . . . substitute for y in the second eqn
... <u>Step 3</u>: 7x = 14 . . . . . add 10
... <u>Step 4</u>: x = 2 . . . . . . . divide by 7
... <u>Step 5</u>: 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.
