1 answer:
Pick 2 pairs of equations t<span>hen use addition and subtraction to eliminate </span>the same variable<span> from both pairs of equations then it is left with 2 variables </span>Pick two pairs <span><span>4x - 3y + z = - 10</span><span>2x + y + 3z = 0 </span></span>eliminate the same variable from each system <span><span>4x - 3y + z = - 10</span> <span>2x + y + 3z = 0</span> <span>4x - 3y + z = - 10</span> <span>-4x - 2y - 6z = 0</span> <span>-5y - 5z = - 10</span> <span>2x + y + 3z = 0</span> <span>- x + 2y - 5z = 17</span> <span>2x + y + 3z = 0</span> <span>-2x + 4y - 10z = 34</span> <span>5y - 7z = 34 </span></span>Solve the system of the two new equations: <span><span>-5y - 5z = - 10</span> <span>5y - 7z = 34</span> <span>-12z = 24</span> which is , <span>z = - 2</span> <span>-5y - 5(- 2) = - 10</span> <span>-5y = - 20</span> wich is , <span>y = 4 </span></span>substitute into one of the original equations <span>- x + 2y - 5z = 17</span> <span>- x + 2(4) - 5(- 2) = 17</span> <span>- x + 18 = 17</span> <span>- x = - 1</span> <span>x = 1</span> <span>which is , </span><span>(x, y, z) = (1, 4, - 2)</span><span> </span>Does 2(1) + 4 + 3(- 2) = 0<span> ? Yes</span><span> </span>
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