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Solve the system -3x+y=7;5x+2y=3 using substitution.
Using substitution, you solve one of the equations for one of the variables. It is often easiest to choose the variable with a coefficient of 1 if there is one. In the first of the equations, y has 1 as a coefficient, so solve the first equation for y:
-3x+y=7 ==> y=3x+7
Now we take that expression for y and substitute it for y in the second equation:
If ` `x=-1 then y=3x+7=` `3(-1)+7=4
Thus the solution is x=-1,y=4
We can check by substituting into the original equations:
` `5(-1)+2(4)=-5+8=3 as required.
The equations are: -3x+y=7 ----(i)
and 5x+2y=3 ----(ii)
From equation (i) -3x+y=7
or, 3x =y-7
Substituting the value of x in equation (ii), we get
`5(y-7)/3 + 2y = 3`
or, `(5y-35)/3 + 2y = 3`
or, `(5y-35+6y)/3 = 3`
or, 11y - 35 = ` `9
or, 11y = 9+35 = 44
or, y = 44/11 = 4.
Now, putting this value of y in equation (i) we get,
-3x + 4 = 7
or, -3x = 7-4 = 3
or, x = 3/-3 = -1.
Therefore, solution of these two equations with respect to x and y yields x = -1, and y = 4.
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