SOLUTION: Solve by substitution. -4x+y= -11 2x-3y= 5 I started by isolating "x" in 2nd equation: 2x = 3y+5. I substituted the "x" in the 1st equation: -4(3y+5)+y+ -11 to get: -12y

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve by substitution. -4x+y= -11 2x-3y= 5 I started by isolating "x" in 2nd equation: 2x = 3y+5. I substituted the "x" in the 1st equation: -4(3y+5)+y+ -11 to get: -12y      Log On


   

Question 100795This question is from textbook Intro Alg
: Solve by substitution.
-4x+y= -11
2x-3y= 5
I started by isolating "x" in 2nd equation: 2x = 3y+5. I substituted the "x" in the 1st equation: -4(3y+5)+y+ -11 to get: -12y-20+y= -11.
I combined like terms to get: -11y = 9 , to get the solution for "y" - 9/11. Is this correct? If so, how do I get "x" solution? This question is from textbook Intro Alg

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%2B1%2Ay=-11
2%2Ax-3%2Ay=5

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%2B4%2AxAdd 4%2Ax to both sides

y=%28-11%2B4%2Ax%29 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.


2%2Ax%2B-3%2Ahighlight%28%28-11%2B4%2Ax%29%29=5 Replace y with -11%2B4%2Ax. Since this eliminates y, we can now solve for x.

2%2Ax-3%2A%28-11%29-3%284%29x=5 Distribute -3 to -11%2B4%2Ax

2%2Ax%2B33-12%2Ax=5 Multiply



2%2Ax%2B33-12%2Ax=5 Reduce any fractions

2%2Ax-12%2Ax=5-33 Subtract 33 from both sides


2%2Ax-12%2Ax=-28 Combine the terms on the right side



-10%2Ax=-28 Now combine the terms on the left side.


cross%28%281%2F-10%29%28-10%2F1%29%29x=%28-28%2F1%29%281%2F-10%29 Multiply both sides by 1%2F-10. This will cancel out -10%2F1 and isolate x

So when we multiply -28%2F1 and 1%2F-10 (and simplify) we get



x=14%2F5 <---------------------------------One answer

Now that we know that x=14%2F5, lets substitute that in for x to solve for y

2%2814%2F5%29-3%2Ay=5 Plug in x=14%2F5 into the 2nd equation

28%2F5-3%2Ay=5 Multiply

-3%2Ay=5-28%2F5Subtract 28%2F5 from both sides

-3%2Ay=25%2F5-28%2F5 Make 5 into a fraction with a denominator of 5



-3%2Ay=-3%2F5 Combine the terms on the right side

cross%28%281%2F-3%29%28-3%29%29%2Ay=%28-3%2F5%29%281%2F-3%29 Multiply both sides by 1%2F-3. This will cancel out -3 on the left side.

y=-3%2F-15 Multiply the terms on the right side


y=1%2F5 Reduce


So this is the other answer


y=1%2F5<---------------------------------Other answer


So our solution is

x=14%2F5 and y=1%2F5

which can also look like

(14%2F5,1%2F5)

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

-4%2Ax%2B1%2Ay=-11
2%2Ax-3%2Ay=5

we get


graph of -4%2Ax%2B1%2Ay=-11 (red) and 2%2Ax-3%2Ay=5 (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 (14%2F5,1%2F5). This verifies our answer.


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Check:

Plug in (14%2F5,1%2F5) into the system of equations


Let x=14%2F5 and y=1%2F5. Now plug those values into the equation -4%2Ax%2B1%2Ay=-11

-4%2A%2814%2F5%29%2B1%2A%281%2F5%29=-11 Plug in x=14%2F5 and y=1%2F5


-56%2F5%2B1%2F5=-11 Multiply


-55%2F5=-11 Add


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


So the solution (14%2F5,1%2F5) satisfies -4%2Ax%2B1%2Ay=-11



Let x=14%2F5 and y=1%2F5. Now plug those values into the equation 2%2Ax-3%2Ay=5

2%2A%2814%2F5%29-3%2A%281%2F5%29=5 Plug in x=14%2F5 and y=1%2F5


28%2F5-3%2F5=5 Multiply


25%2F5=5 Add


5=5 Reduce. Since this equation is true the solution works.


So the solution (14%2F5,1%2F5) satisfies 2%2Ax-3%2Ay=5


Since the solution (14%2F5,1%2F5) satisfies the system of equations


-4%2Ax%2B1%2Ay=-11
2%2Ax-3%2Ay=5


this verifies our answer.