SOLUTION: I really really need help and I've been searching over the internet for the best source to hepl me unfortunately my school exam on this is tomorrow. But it would really help to kno

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Question 119540This question is from textbook Algebra II
: I really really need help and I've been searching over the internet for the best source to hepl me unfortunately my school exam on this is tomorrow. But it would really help to know how to do the problems. My main problem is in Chapter 3 of my book , on Solving Linear Systems Alegraically. I don't understand anything about it, it just confuses me .
such as 3x + 4y equals -4
x + 2y equals 2
and in the book it says to solve the linear system using the substituion method.
I'm having problems on problems like that and on graphing in section 3.3 of my book on Graphing and Solving Systems of Linear inequalities.

on pages 159 and 148 mostly those pages
THanks! This question is from textbook Algebra II

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

3%2Ax%2B4%2Ay=-4
1%2Ax%2B2%2Ay=2

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

4%2Ay=-4-3%2AxSubtract 3%2Ax from both sides

y=%28-4-3%2Ax%29%2F4 Divide both sides by 4.


Which breaks down and reduces to



y=-1-%283%2F4%29%2Ax Now we've fully isolated y

Since y equals -1-%283%2F4%29%2Ax we can substitute the expression -1-%283%2F4%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


1%2Ax%2B2%2Ahighlight%28%28-1-%283%2F4%29%2Ax%29%29=2 Replace y with -1-%283%2F4%29%2Ax. Since this eliminates y, we can now solve for x.

1%2Ax%2B2%2A%28-1%29%2B2%28-3%2F4%29x=2 Distribute 2 to -1-%283%2F4%29%2Ax

1%2Ax-2-%286%2F4%29%2Ax=2 Multiply



1%2Ax-2-%283%2F2%29%2Ax=2 Reduce any fractions

1%2Ax-%283%2F2%29%2Ax=2%2B2Add 2 to both sides


1%2Ax-%283%2F2%29%2Ax=4 Combine the terms on the right side



%282%2F2%29%2Ax-%283%2F2%29x=4 Make 1 into a fraction with a denominator of 2

%28-1%2F2%29%2Ax=4 Now combine the terms on the left side.


cross%28%282%2F-1%29%28-1%2F2%29%29x=%284%2F1%29%282%2F-1%29 Multiply both sides by 2%2F-1. This will cancel out -1%2F2 and isolate x

So when we multiply 4%2F1 and 2%2F-1 (and simplify) we get



x=-8 <---------------------------------One answer

Now that we know that x=-8, lets substitute that in for x to solve for y

1%28-8%29%2B2%2Ay=2 Plug in x=-8 into the 2nd equation

-8%2B2%2Ay=2 Multiply

2%2Ay=2%2B8Add 8 to both sides

2%2Ay=10 Combine the terms on the right side

cross%28%281%2F2%29%282%29%29%2Ay=%2810%2F1%29%281%2F2%29 Multiply both sides by 1%2F2. This will cancel out 2 on the left side.

y=10%2F2 Multiply the terms on the right side


y=5 Reduce


So this is the other answer


y=5<---------------------------------Other answer


So our solution is

x=-8 and y=5

which can also look like

(-8,5)

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

3%2Ax%2B4%2Ay=-4
1%2Ax%2B2%2Ay=2

we get


graph of 3%2Ax%2B4%2Ay=-4 (red) and 1%2Ax%2B2%2Ay=2 (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 (-8,5). This verifies our answer.


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Check:

Plug in (-8,5) into the system of equations


Let x=-8 and y=5. Now plug those values into the equation 3%2Ax%2B4%2Ay=-4

3%2A%28-8%29%2B4%2A%285%29=-4 Plug in x=-8 and y=5


-24%2B20=-4 Multiply


-4=-4 Add


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


So the solution (-8,5) satisfies 3%2Ax%2B4%2Ay=-4



Let x=-8 and y=5. Now plug those values into the equation 1%2Ax%2B2%2Ay=2

1%2A%28-8%29%2B2%2A%285%29=2 Plug in x=-8 and y=5


-8%2B10=2 Multiply


2=2 Add


2=2 Reduce. Since this equation is true the solution works.


So the solution (-8,5) satisfies 1%2Ax%2B2%2Ay=2


Since the solution (-8,5) satisfies the system of equations


3%2Ax%2B4%2Ay=-4
1%2Ax%2B2%2Ay=2


this verifies our answer.