7x - 2y = 4 5y + 3x = 10

7x-2y=4

3x+5y=10

so we can eliminate

eliminate y's

2 times 5=10

multiply first by 5 and 2nd by 2 and add

35x-10y=20

6x+10y=20 +

41x+0y=40

41x=40

divide both sides by 41

x=40/41

sub back

7x-2y=4

solve for y first to make it easier

-2y=4-7x

y = (7/2) x-2

y = (7/2) (40/41) - 2

y = (280/82) - 2

y=140/41-2

y=140/41-82/41

y=58/41

(x, y)

(40/41,58/41)