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-14x + 19y = 46

14x - 9y = 102        add the two  equations

10y  = 148            divide both sides by 10

y = 148/10   =   74/5        substitute this for y in either equation  [ I'll use the second ]

14x - 9[74/5]   = 102       multiply through by  5

70x - 9(74)  =  510

70x - 666  = 510        add 666 to both sides

70x = 1176             divide both sides by 70

x = 1176 / 70  = 588/35  = 84/5

It is -5.6 =Y and 3.7 =X I rounded to the nearest tenth.

how'd you get that?

Solve the following system:
{19 y-14 x = 46 |     (equation 1)
14 x-9 y = 102 |     (equation 2)
Add equation 1 to equation 2:
{-(14 x)+19 y = 46 |     (equation 1)
0 x+10 y = 148 |     (equation 2)
Divide equation 2 by 2:
{-(14 x)+19 y = 46 |     (equation 1)
0 x+5 y = 74 |     (equation 2)
Divide equation 2 by 5:
{-(14 x)+19 y = 46 |     (equation 1)
0 x+y = 74/5 |     (equation 2)
Subtract 19 × (equation 2) from equation 1:
{-(14 x)+0 y = (-1176)/5 |     (equation 1)
0 x+y = 74/5 |     (equation 2)
Divide equation 1 by -14:
{x+0 y = 84/5 |     (equation 1)
0 x+y = 74/5 |     (equation 2)
Collect results:
Answer: | x = 84/5          and              y = 74/5