SOLUTION: Please help solve by substitution 9x+5y=28 3x+9y=-42 Please show all your steps, I doing something wrong and can't seem to figure out what it is. thank you in advance for the

Algebra ->  Linear-equations -> SOLUTION: Please help solve by substitution 9x+5y=28 3x+9y=-42 Please show all your steps, I doing something wrong and can't seem to figure out what it is. thank you in advance for the      Log On


   

Question 125259: Please help solve by substitution
9x+5y=28
3x+9y=-42
Please show all your steps, I doing something wrong and can't seem to figure out what it is. thank you in advance for the help
Answer by MathLover1(20849) 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

9%2Ax%2B5%2Ay=28
3%2Ax%2B9%2Ay=-42

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

5%2Ay=28-9%2AxSubtract 9%2Ax from both sides

y=%2828-9%2Ax%29%2F5 Divide both sides by 5.


Which breaks down and reduces to



y=28%2F5-%289%2F5%29%2Ax Now we've fully isolated y

Since y equals 28%2F5-%289%2F5%29%2Ax we can substitute the expression 28%2F5-%289%2F5%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


3%2Ax%2B9%2Ahighlight%28%2828%2F5-%289%2F5%29%2Ax%29%29=-42 Replace y with 28%2F5-%289%2F5%29%2Ax. Since this eliminates y, we can now solve for x.

3%2Ax%2B9%2A%2828%2F5%29%2B9%28-9%2F5%29x=-42 Distribute 9 to 28%2F5-%289%2F5%29%2Ax

3%2Ax%2B252%2F5-%2881%2F5%29%2Ax=-42 Multiply



3%2Ax%2B252%2F5-%2881%2F5%29%2Ax=-42 Reduce any fractions

3%2Ax-%2881%2F5%29%2Ax=-42-252%2F5 Subtract 252%2F5 from both sides


3%2Ax-%2881%2F5%29%2Ax=-210%2F5-252%2F5 Make -42 into a fraction with a denominator of 5


3%2Ax-%2881%2F5%29%2Ax=-462%2F5 Combine the terms on the right side



%2815%2F5%29%2Ax-%2881%2F5%29x=-462%2F5 Make 3 into a fraction with a denominator of 5

%28-66%2F5%29%2Ax=-462%2F5 Now combine the terms on the left side.


cross%28%285%2F-66%29%28-66%2F5%29%29x=%28-462%2F5%29%285%2F-66%29 Multiply both sides by 5%2F-66. This will cancel out -66%2F5 and isolate x

So when we multiply -462%2F5 and 5%2F-66 (and simplify) we get



x=7 <---------------------------------One answer

Now that we know that x=7, lets substitute that in for x to solve for y

3%287%29%2B9%2Ay=-42 Plug in x=7 into the 2nd equation

21%2B9%2Ay=-42 Multiply

9%2Ay=-42-21Subtract 21 from both sides

9%2Ay=-63 Combine the terms on the right side

cross%28%281%2F9%29%289%29%29%2Ay=%28-63%2F1%29%281%2F9%29 Multiply both sides by 1%2F9. This will cancel out 9 on the left side.

y=-63%2F9 Multiply the terms on the right side


y=-7 Reduce


So this is the other answer


y=-7<---------------------------------Other answer


So our solution is

x=7 and y=-7

which can also look like

(7,-7)

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

9%2Ax%2B5%2Ay=28
3%2Ax%2B9%2Ay=-42

we get


graph of 9%2Ax%2B5%2Ay=28 (red) and 3%2Ax%2B9%2Ay=-42 (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 (7,-7). This verifies our answer.


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Check:

Plug in (7,-7) into the system of equations


Let x=7 and y=-7. Now plug those values into the equation 9%2Ax%2B5%2Ay=28

9%2A%287%29%2B5%2A%28-7%29=28 Plug in x=7 and y=-7


63-35=28 Multiply


28=28 Add


28=28 Reduce. Since this equation is true the solution works.


So the solution (7,-7) satisfies 9%2Ax%2B5%2Ay=28



Let x=7 and y=-7. Now plug those values into the equation 3%2Ax%2B9%2Ay=-42

3%2A%287%29%2B9%2A%28-7%29=-42 Plug in x=7 and y=-7


21-63=-42 Multiply


-42=-42 Add


-42=-42 Reduce. Since this equation is true the solution works.


So the solution (7,-7) satisfies 3%2Ax%2B9%2Ay=-42


Since the solution (7,-7) satisfies the system of equations


9%2Ax%2B5%2Ay=28
3%2Ax%2B9%2Ay=-42


this verifies our answer.