SOLUTION: I need your help solving this problem: solve: {4x-y =11 {x+2y = -4 Is this the case where I substitute 0 for y in the first equation and solve for x and th

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Question 92802: I need your help solving this problem:

solve: {4x-y =11
{x+2y = -4

Is this the case where I substitute 0 for y in the first equation and solve for x and then substitute 0 for x in the second equation and solve for y? Or do I use the value for x from the first equation to plug into the second equation? I am confused. Thanks for your help. Barineau
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

4%2Ax-1%2Ay=11
1%2Ax%2B2%2Ay=-4

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

Solve for y for the first equation

-1%2Ay=11-4%2AxSubtract 4%2Ax from both sides

y=%2811-4%2Ax%29%2F-1 Divide both sides by -1.


Which breaks down and reduces to



y=-11%2B4%2Ax Now we've fully isolated y

Since y equals -11%2B4%2Ax we can substitute the expression -11%2B4%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


1%2Ax%2B2%2Ahighlight%28%28-11%2B4%2Ax%29%29=-4 Replace y with -11%2B4%2Ax. Since this eliminates y, we can now solve for x.

1%2Ax%2B2%2A%28-11%29%2B2%284%29x=-4 Distribute 2 to -11%2B4%2Ax

1%2Ax-22%2B8%2Ax=-4 Multiply



1%2Ax-22%2B8%2Ax=-4 Reduce any fractions

1%2Ax%2B8%2Ax=-4%2B22Add 22 to both sides


1%2Ax%2B8%2Ax=18 Combine the terms on the right side



9%2Ax=18 Now combine the terms on the left side.


cross%28%281%2F9%29%289%2F1%29%29x=%2818%2F1%29%281%2F9%29 Multiply both sides by 1%2F9. This will cancel out 9%2F1 and isolate x

So when we multiply 18%2F1 and 1%2F9 (and simplify) we get



x=2 <---------------------------------One answer

Now that we know that x=2, lets substitute that in for x to solve for y

1%282%29%2B2%2Ay=-4 Plug in x=2 into the 2nd equation

2%2B2%2Ay=-4 Multiply

2%2Ay=-4-2Subtract 2 from both sides

2%2Ay=-6 Combine the terms on the right side

cross%28%281%2F2%29%282%29%29%2Ay=%28-6%2F1%29%281%2F2%29 Multiply both sides by 1%2F2. This will cancel out 2 on the left side.

y=-6%2F2 Multiply the terms on the right side


y=-3 Reduce


So this is the other answer


y=-3<---------------------------------Other answer


So our solution is

x=2 and y=-3

which can also look like

(2,-3)

Notice if we graph the equations (if you need help with graphing, check out this solver)

4%2Ax-1%2Ay=11
1%2Ax%2B2%2Ay=-4

we get


graph of 4%2Ax-1%2Ay=11 (red) and 1%2Ax%2B2%2Ay=-4 (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.


and we can see that the two equations intersect at (2,-3). This verifies our answer.


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Check:

Plug in (2,-3) into the system of equations


Let x=2 and y=-3. Now plug those values into the equation 4%2Ax-1%2Ay=11

4%2A%282%29-1%2A%28-3%29=11 Plug in x=2 and y=-3


8%2B3=11 Multiply


11=11 Add


11=11 Reduce. Since this equation is true the solution works.


So the solution (2,-3) satisfies 4%2Ax-1%2Ay=11



Let x=2 and y=-3. Now plug those values into the equation 1%2Ax%2B2%2Ay=-4

1%2A%282%29%2B2%2A%28-3%29=-4 Plug in x=2 and y=-3


2-6=-4 Multiply


-4=-4 Add


-4=-4 Reduce. Since this equation is true the solution works.


So the solution (2,-3) satisfies 1%2Ax%2B2%2Ay=-4


Since the solution (2,-3) satisfies the system of equations


4%2Ax-1%2Ay=11
1%2Ax%2B2%2Ay=-4


this verifies our answer.