How many solutions does the system of equations $5 x - 4 y = - 8$ $5x - 4y = - 8$ and $17 x + 3 y = - 12$ $17x + 3y = - 12$ have?

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Answer 1 · 2018-02-08T17:15:06

There is one solution to the system, but 2 answers (x and y).

Solve first by getting a common base (same coefficient)

$5 x - 4 y = - 8$ $5x-4y=-8$ to $15 x - 12 y = - 24$ $15x-12y=-24$ (multiply by 3)

$17 x + 3 y = - 12$ $17x+3y=-12$ to $68 x + 12 y = - 48$ $68x+12y=-48$ (multiply by 4)

Solve with elimination (add the 2 equations together):

$83 x = - 72$ $83x=-72$

$\frac{83 x}{83} = \frac{- 72}{83}$ $(83x)/83=(-72)/83$

$x = - \frac{72}{83}$ $x=-72/83$

$5 \cdot (- \frac{72}{83}) - 4 y = - 8$ $5*(-72/83)-4y=-8$

$- 4 y \approx 4.34$ $-4y~~4.34$

$y \approx 1.084$ $y~~1.084$

There is one solution to the system, but 2 answers (x and y)

How many solutions does the system of equations 5x - 4y = - 85x−4y=−85x - 4y = - 8 and 17x + 3y = - 1217x+3y=−1217x + 3y = - 12 have?