SOLUTION: Determine which of the following points are solutions to the system of equations. {3x – y = -4 {2x – 5y = 19 A. (−3, 5) B. (3, −5) C. (3, 5) D. (−3, &#8

Algebra ->  Expressions -> SOLUTION: Determine which of the following points are solutions to the system of equations. {3x – y = -4 {2x – 5y = 19 A. (−3, 5) B. (3, −5) C. (3, 5) D. (−3, &#8      Log On


   

Question 827924: Determine which of the following points are solutions to the system of equations.
{3x – y = -4
{2x – 5y = 19
A. (−3, 5)
B. (3, −5)
C. (3, 5)
D. (−3, −5)
Please Show Work
Answer by MathLover1(20850) 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-1%2Ay=-4
2%2Ax-5%2Ay=19

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

y=%28-4-3%2Ax%29%2F-1 Divide both sides by -1.


Which breaks down and reduces to



y=4%2B3%2Ax Now we've fully isolated y

Since y equals 4%2B3%2Ax we can substitute the expression 4%2B3%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


2%2Ax%2B-5%2Ahighlight%28%284%2B3%2Ax%29%29=19 Replace y with 4%2B3%2Ax. Since this eliminates y, we can now solve for x.

2%2Ax-5%2A%284%29-5%283%29x=19 Distribute -5 to 4%2B3%2Ax

2%2Ax-20-15%2Ax=19 Multiply



2%2Ax-20-15%2Ax=19 Reduce any fractions

2%2Ax-15%2Ax=19%2B20Add 20 to both sides


2%2Ax-15%2Ax=39 Combine the terms on the right side



-13%2Ax=39 Now combine the terms on the left side.


cross%28%281%2F-13%29%28-13%2F1%29%29x=%2839%2F1%29%281%2F-13%29 Multiply both sides by 1%2F-13. This will cancel out -13%2F1 and isolate x

So when we multiply 39%2F1 and 1%2F-13 (and simplify) we get



x=-3 <---------------------------------One answer

Now that we know that x=-3, lets substitute that in for x to solve for y

2%28-3%29-5%2Ay=19 Plug in x=-3 into the 2nd equation

-6-5%2Ay=19 Multiply

-5%2Ay=19%2B6Add 6 to both sides

-5%2Ay=25 Combine the terms on the right side

cross%28%281%2F-5%29%28-5%29%29%2Ay=%2825%2F1%29%281%2F-5%29 Multiply both sides by 1%2F-5. This will cancel out -5 on the left side.

y=25%2F-5 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=-3 and y=-5

which can also look like

(-3,-5)

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

3%2Ax-1%2Ay=-4
2%2Ax-5%2Ay=19

we get


graph of 3%2Ax-1%2Ay=-4 (red) and 2%2Ax-5%2Ay=19 (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 (-3,-5). This verifies our answer.


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Check:

Plug in (-3,-5) into the system of equations


Let x=-3 and y=-5. Now plug those values into the equation 3%2Ax-1%2Ay=-4

3%2A%28-3%29-1%2A%28-5%29=-4 Plug in x=-3 and y=-5


-9%2B5=-4 Multiply


-4=-4 Add


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


So the solution (-3,-5) satisfies 3%2Ax-1%2Ay=-4



Let x=-3 and y=-5. Now plug those values into the equation 2%2Ax-5%2Ay=19

2%2A%28-3%29-5%2A%28-5%29=19 Plug in x=-3 and y=-5


-6%2B25=19 Multiply


19=19 Add


19=19 Reduce. Since this equation is true the solution works.


So the solution (-3,-5) satisfies 2%2Ax-5%2Ay=19


Since the solution (-3,-5) satisfies the system of equations


3%2Ax-1%2Ay=-4
2%2Ax-5%2Ay=19


this verifies our answer.





so, answer is D. (−3, −5)