SOLUTION: solve by the substatution method 2x+4y=26 -2x+y=19 the solution is ___________ __

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: solve by the substatution method 2x+4y=26 -2x+y=19 the solution is ___________ __      Log On

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Question 407511: solve by the substatution method
the solution is ______________

Answer by jim_thompson5910(33401) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

-2x%2By=19 Start with the first equation

y=19%2B2x Add 2x to both sides

y=2x%2B19 Rearrange the equation


Since y=2x%2B19, we can now replace each y in the second equation with 2x%2B19 to solve for x

2x%2B4highlight%28%282x%2B19%29%29=26 Plug in y=2x%2B19 into the second equation. In other words, replace each y with 2x%2B19. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.

2x%2B%284%29%282%29x%2B%284%29%2819%29=26 Distribute 4 to 2x%2B19

2x%2B8x%2B76=26 Multiply

10x%2B76=26 Combine like terms on the left side

10x=26-76Subtract 76 from both sides

10x=-50 Combine like terms on the right side

x=%28-50%29%2F%2810%29 Divide both sides by 10 to isolate x

x=-5 Divide

-----------------First Answer------------------------------

So the first part of our answer is: x=-5

Since we know that x=-5 we can plug it into the equation y=2x%2B19 (remember we previously solved for y in the first equation).

y=2x%2B19 Start with the equation where y was previously isolated.

y=2%28-5%29%2B19 Plug in x=-5

y=-10%2B19 Multiply

y=9 Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is: y=9


So our answers are:

x=-5 and y=9

which form the point

Now let's graph the two equations (if you need help with graphing, check out this solver)

From the graph, we can see that the two equations intersect at . This visually verifies our answer.

graph of -2x%2By=19 (red) and 2x%2B4y=26 (green) and the intersection of the lines (blue circle).

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