Solve 2x+y=23 and 4x-y=19 , find the value of x-3y and 5y-x
Elemination Method
Given Equations are,
2x+y=23 — (i)
4x-y=19 —(ii)
Addding Equations (i) and (ii) we get,
2x+y + 4x-y=23+19
⟹ 6x = 42
⟹ x = $\frac{42}{6}$
⟹ x = 7
Substituting the value of x in equation (i) we get,
2(7)+y=23
⟹ 14 +y =23
⟹ y=23-14
⟹ y=9
∴ Required Solutions are x = 7 and y = 9
∴ x-3y =7-3(9)=7-27= -20
and 5y-x =5(9)-7=45-7=38
Substituting Method
2x+y=23 — (i)
From equation (i) we get,
y = 23 -2x —(iii)
Substituting the value of y in equation (ii) we get,
4x-(23-2x)=19
⟹ 4x -23+2x=19
⟹ 6x =23+19
⟹ 6x=42
⟹ x = $\frac{42}{6}$
⟹ x =7
Now from equation (iii) we get,
y = 23-2(7)
⟹ y = 23-14
⟹ y = 9
∴ Required Solutions are x = 7 and y = 9
∴ x-3y =7-3(9)=7-27= -20
and 5y-x =5(9)-7=45-7=38