SOLUTION: 7. Solve the following system of equations using substitution, elimination, or graphing. Please and Thank you. y=2x+6 2y+3x=5

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 7. Solve the following system of equations using substitution, elimination, or graphing. Please and Thank you. y=2x+6 2y+3x=5      Log On


   

Question 159294: 7. Solve the following system of equations using substitution, elimination, or graphing. Please and Thank you.
y=2x+6
2y+3x=5
Found 2 solutions by jim_thompson5910, jojo14344:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system

y=2x%2B6
2y%2B3x=5



2%282x%2B6%29%2B3x=5 Plug in y=2x%2B6 into the second equation. In other words, replace each y with 2x%2B6. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


4x%2B12%2B3x=5 Distribute


7x%2B12=5 Combine like terms on the left side


7x=5-12Subtract 12 from both sides


7x=-7 Combine like terms on the right side


x=%28-7%29%2F%287%29 Divide both sides by 7 to isolate x



x=-1 Divide




Now that we know that x=-1, we can plug this into y=2x%2B6 to find y



y=2%28-1%29%2B6 Substitute -1 for each x


y=-2%2B6 Multiply


y=4 Add


So our answer is x=-1 and y=4 which forms the ordered pair



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


Graph of 2y%2B3x=5 (red) and y=2x%2B6 (green)



Questions? Email me at jim_thompson5910@hotmail.com


Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

y=2x%2B6 ----------------> eqn 1
2y%2B3x=5 ---------------> eqn 2
Substitute eqn 1 in eqn 2:
2%282x%2B6%29%2B3x=5, distribution
4x%2B12%2B3x=5
7x=5-12=-7
cross%287%29x%2Fcross%287%29=cross%28-7%291%2Fcross%287%29
x=-1,
For y via eqn 1:
y=2%28-1%29%2B6=-2%2B6
y=4
Check it out via eqn 2:
2%284%29%2B3%28-1%29=5
8-3=5
5=5
See graph below:
-----> see the intersection at point (-1,4). Then our answers are right.
Thank you,
Jojo