Solve the following system of equations by using the substitution method. x = y + 3 2x + y = 9

3 Answers

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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Using substitution to solve for x and y:

The first equation is already in a suitable format:   x= y+3

Therefore we can substitute straight into the second:

2x+y=9 becomes 2(y+3) +y=9

`therefore 2y+6+y=9`

Now solve for y

`therefore 3y=9-6`

`therefore y=3/3`

`therefore y=1`

Now use your original equation to find x

`therefore x=y+3` becomes `x=1+3`

`therefore x=4`

Ans:(4;1) x=4 y=1

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jmelchior | College Teacher | (Level 1) eNoter

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What we need to do is to use one of the equations to give us enoguh information to solve the other.  For example, we have,

x = y+3

Knowing this, we can replace all the x in the second equation with y+3,

2(y+3) + y = 9

Notice that we now only have to solve for one variable - y - instead of x and y.  This gives,
3y + 6 = 9
3y = 3
y = 1

Now that we have a value for y, we can substitute it into your equations to solve for x,

x = y + 3
x = (1) + 3
x = 4

Notice that y = 4 and x = 1 solves both of your equations at the same time.

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user4825270 | Student | (Level 3) eNoter

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let x=y+3 be equation 1 and 2x+y=9 be equation 2
by the substitution method, x is already the subject in eqn. 1 so we simply substitute it into eqn. 2 this gives us......
knowing the value of y,