SOLUTION: Solve the linear system y = x + 7 2x + 3y = 31 (hint: substitution)

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Question 143307This question is from textbook
: Solve the linear system
y = x + 7
2x + 3y = 31 (hint: substitution) This question is from textbook

Found 2 solutions by nabla, jim_thompson5910:
Answer by nabla(475) (Show Source):
You can put this solution on YOUR website!
The problem is already solved for y in the first equation. Put that into the second and solve...
ie 2x + 3y = 31
^substitute x+7 for y
2x + 3(x+7)=31
5x=10
x=2
If x=2, y must be 9.
Check:
x+7-->2+7=9 yes
2x+3y=2(2)+3(9)=4+27=31 yes
And here is how this site's solver would do it:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve:
We'll use substitution. After moving -1*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: So, we know that y=9. Since , x=2.

Answer: .

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given system

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute

Combine like terms on the left side

Subtract 21 from both sides

Combine like terms on the right side

Divide both sides by 5 to isolate x

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and which also looks like

Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.

Graph of (red) and (green)