<nobr id="r1bpv"><listing id="r1bpv"><menuitem id="r1bpv"></menuitem></listing></nobr>
<pre id="r1bpv"></pre>
      <address id="r1bpv"></address>

      <em id="r1bpv"><sub id="r1bpv"><video id="r1bpv"></video></sub></em> <em id="r1bpv"><address id="r1bpv"></address></em>
        <th id="r1bpv"><noframes id="r1bpv">

          <meter id="r1bpv"></meter>
            Paul's Online Notes
            Paul's Online Notes
            Home / Algebra Trig Review / Algebra / Solving Equations, Part II
            Show Mobile Notice Show All Notes Hide All Notes
            Mobile Notice
            You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

            Solving Equations, Part II

            Solve each of the following equations for \(y\).Show All Solutions Hide All Solutions

            1. \(\displaystyle x = \frac{{2y - 5}}{{6 - 7y}}\)
              Show Solution

              Here all we need to do is get all the \(y\)’s on one side, factor a \(y\) out and then divide by the coefficient of the \(y\)

              \[\begin{align*}x & = \frac{{2y - 5}}{{6 - 7y}}\\ x\left( {6 - 7y} \right) & = 2y - 5\\ 6x - 7xy & = 2y - 5\\ 6x + 5 & = \left( {7x + 2} \right)y\\ y & = \frac{{6x + 5}}{{7x + 2}}\end{align*}\]

              Solving equations for one of the variables in it is something that you’ll be doing on occasion in a Calculus class so make sure that you can do it.

            2. \(3{x^2}\left( {3 - 5y} \right) + \sin x = 3xy + 8\)
              Show Solution

              This one solves the same way as the previous problem.

              \[\begin{align*}3{x^2}\left( {3 - 5y} \right) + \sin x & = 3xy + 8\\ 9{x^2} - 15{x^2}y + \sin x & = 3xy + 8\\ 9{x^2} + \sin x - 8 & = \left( {3x + 15{x^2}} \right)y\\ y & = \frac{{9{x^2} + \sin x - 8}}{{3x + 15{x^2}}}\end{align*}\]
            3. \(2{x^2} + 2{y^2} = 5\)
              Show Solution

              Same thing, just be careful with the last step.

              \[\begin{align*}2{x^2} + 2{y^2} & = 5\\ 2{y^2} & = 5 - 2{x^2}\\ {y^2} & = \frac{1}{2}\left( {5 - 2{x^2}} \right)\\ y & = \pm \sqrt {\frac{5}{2} - {x^2}} \end{align*}\]

              Don’t forget the “\( \pm \)” in the solution!

            天天干夜夜爱 天天色播 天天射天天舔 <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <蜘蛛词>| <文本链> <文本链> <文本链> <文本链> <文本链> <文本链>