How to solve step by step -3x+y=7, 5x+2y=3 using the systems of equations substitution method

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embizze | High School Teacher | (Level 1) Educator Emeritus

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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:

5x+2(3x+7)=3

5x+6x+14=3

11x=-11

` `x=-1

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:

` `-3(-1)+4=3+4=7

` `5(-1)+2(4)=-5+8=3 as required.

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mathewww | High School Teacher | (Level 1) Honors

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The equations are: -3x+y=7 ----(i)

and 5x+2y=3 ----(ii)

From equation (i) -3x+y=7

or, 3x =y-7

or, `x=(y-7)/3`

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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