SOLUTION: 50.Solve the system by substitution. 3x + 3y = 9 y = 2x � 12

Question 75571: 50.Solve the system by substitution.
3x + 3y = 9
y = 2x � 12

Found 3 solutions by bucky, chitra, jim_thompson5910:
Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!
3x + 3y = 9
y = 2x � 12
.
From the bottom equation, you know what y (the left side) is in terms of x (the right side
of the equation). So you can use the right side of the bottom equation as a replacement
for y in the top equation. When you make that substitution, the top equation becomes:
.
3x + 3(2x - 12) = 9
.
Multiply out the left side to get:
.
3x + 6x - 36 = 9
.
combine the x terms:
.
9x - 36 = 9
.
Add 36 to both sides to eliminate the -36 on the left side, and you get:
.
9x = 9 + 36
.
which simplifies to:
.
9x = 45
.
Solve for x by dividing both sides by 9 and you get:
.
x = 5
.
And from the bottom equation you know that y = 2x - 12. Substitute 5 for x and the equation
becomes y = 2*5 - 12 = 10 - 12 = -2
.
So the answer to your problem is that for the two given equations, (5, -2) is a common solution
meaning that x = 5, y = 2 is a common point whose values will make both of the given equations
true.
.
The rule for finding the common solution to a pair of linear equations begins with solving
one of the two equations for a variable in terms of the other variable. In this problem
that was already done for you in the bottom equation. Then you substitute that solution
into the other equation and solve for the one variable. Then simply substitute that known
value into either of the original equations and solve for the other variable.
.
Hope that helps you to understand how to proceed with a problem such as this.

Answer by chitra(359)   (Show Source): You can put this solution on YOUR website!
The given set of equations are:
3x + 3y = 9 ------------(1)
y = 2x � 12 ------------(2)

Substituting, eqn(2) in eqn(1) we get:

3x + 3(2x - 12) = 9

3x + 6x - 36 = 9

9x = 9 + 36

9x = 45

==> x = 45/9

==> x = 5

Substituting for x in any one of the equations, we get the value of y.

y = 2(5) - 12

y = 10 - 12

y = -2

Hence, the value of x = 5 and y = -2

Thsu, the solution.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Plug this equation into the first one
Substitute 2x-12 into y
Distribute the 3
Combine like terms
Add 36 to both sides
Divide both sides by 9
Use this to find y.

Multiply
Subtract 15 from both sides
Divide both sides by 3
So the solution is (5,-2)

Check:
plug in (5,-2)

works
works
So the solution satisfies the system
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