Thus, [ x = \frac2622= \frac1311\approx1.182,\qquad y = \frac-3822= -\frac1911\approx-1.727. ] (x = \dfrac1311;(\approx1.182),\qquad y = -\dfrac1911;(\approx-1.727))
[ \begincases 3x - 2y = 7\ 5x + 4y = -1 \endcases ] blueprint 4 workbook answer key
The problem tests ability to (a) manipulate linear equations, (b) recognize when elimination yields fractional results, and (c) apply matrix inversion as an alternative verification. Thus, [ x = \frac2622= \frac1311\approx1
[ \beginbmatrixx\y\endbmatrix=A^-1\mathbfb= \frac122 \beginbmatrix 4 & 2\ -5 & 3 \endbmatrix \beginbmatrix7\-1\endbmatrix =\frac122\beginbmatrix 4(7)+2(-1)\ -5(7)+3(-1) \endbmatrix =\frac122\beginbmatrix 28-2\ -35-3 \endbmatrix =\frac122\beginbmatrix 26\ -38 \endbmatrix ] [ x = \frac2622= \frac1311\approx1.182
[ A = \beginbmatrix 3 & -2\ 5 & 4 \endbmatrix,\quad \mathbfb = \beginbmatrix7\-1\endbmatrix ]
(5.6\ \textkW·h=2.016\times10^7\ \textJ)