Hello from MrBillDoesMath!
Answer:
x= 206/23, y = -106/23
Discussion:
4x + 3y = 22 (*)
2x - 10y = 64 (**)
Multiply (**) by 2 and subtract the results from (*)
4x + 3y = 22 (subtract equations)
4x - 20y = 128
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0x + (3y + 20y) = 22 - 128 =>
23y = -106 =>
y = - 106/23
To solve for x:
2x - 10y = 64 =>
2x - 10(-106/23) = 64 =>
2x + 10* 106/23 = 64 =>
2x = 64 - 10*106/23 =>
x = (1/2) ( 64 - 1060/23) =>
x = (1/2) (1472/23 - 1060/23) => (as 64 * 23 = 1472)
x = (1/2) (412/23) = (1/2) 412 * (1/23) = 206/23
Regards,
MrB
