How do you solve the system of equations $4 x - 5 y = 25$ $4x - 5y = 25$ and $- 7 x + 3 y = 8$ $- 7x + 3y = 8$ ?

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Answer 1 · 2018-02-13T14:28:07

$x = - 5 and y = - 9$ $x=-5 and y =-9$

$4 x - 5 y = 25$ $4x - 5y = 25$ ------------(1)

$- 7 x + 3 y = 8$ $- 7x + 3y = 8$ -----------(2)

First eliminate any one variable (say $y$ $y$ ),

$(1) \times 3 + (2) \times 5 \Rightarrow$ $(1) xx 3 + (2) xx 5 =>$

$\Rightarrow 12 x - 15 y - 35 x + 15 y = 75 + 40$ $=>12x - 15y -35x + 15y =75 + 40$

$=> 12x-35x -cancel(15y)+cancel(15y) = 115$

$=> -23 x =115$

$=> x = -5$

Substitute this value of $x$ in any one equation.

(1) $=> 4xx(-5) -5y =25$

$=> -20 -5y =25$

$=> y = (25+20)/-5$

$y = -9$

So, $x=-5 and y =-9$

Verify by substituting both values in equation (2):

Left hand side of equation = $-7x+3y$

$=> -7xx(-5) +3xx(-9) = 35 - 27 = 8$ = Right hand side.

Hence verified.

How do you solve the system of equations 4x - 5y = 254x−5y=254x - 5y = 25 and - 7x + 3y = 8−7x+3y=8 - 7x + 3y = 8?