SOLUTION: Solve using either elimination or substitution. Show your work. If the system has either no solution or an infinite number of solutions, state this. 16x-15y=-10 11x-7y=13

Question 295557: Solve using either elimination or substitution. Show your work. If the system has either no solution or an infinite number of solutions, state this.
16x-15y=-10
11x-7y=13
Answer by edjones(8007) (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

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

Subtract from both sides

Divide both sides by -15.

Which breaks down and reduces to

Now we've fully isolated y

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

Replace y with . Since this eliminates y, we can now solve for x.

Distribute -7 to

Multiply

Reduce any fractions

Add to both sides

Make 13 into a fraction with a denominator of 3

Combine the terms on the right side

Make 11 into a fraction with a denominator of 15

Now combine the terms on the left side.

Multiply both sides by . This will cancel out and isolate x

So when we multiply and (and simplify) we get

<---------------------------------One answer

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

Plug in into the 2nd equation

Multiply

Subtract from both sides

Combine the terms on the right side

Multiply both sides by . This will cancel out -7 on the left side.

Multiply the terms on the right side

Reduce

So this is the other answer

<---------------------------------Other answer

So our solution is

and

which can also look like

(,)

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

we get

graph of (red) and (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 (,). This verifies our answer.

-----------------------------------------------------------------------------------------------
Check:

Plug in (,) into the system of equations

Let and . Now plug those values into the equation

Plug in and

Multiply

Add

Reduce. Since this equation is true the solution works.

So the solution (,) satisfies

Let and . Now plug those values into the equation

Plug in and

Multiply

Add

Reduce. Since this equation is true the solution works.

So the solution (,) satisfies

Since the solution (,) satisfies the system of equations

this verifies our answer.

RELATED QUESTIONS
Solve using either elimination or substitution. Show your work. If the system has either... (answered by drj)

Solve using either elimination or substitution. Show your work. If the system has either... (answered by Alan3354)

I need help with this question. Solve using either elimination or substitution. If the (answered by checkley77)

I need to solve this using either elimination or substitution. If the system has either... (answered by richwmiller)

Help please. 1. Solve using the substitution method. Show your work. If the system has (answered by Fombitz)

solve using the elimination method. show your work if the system has no solution or an... (answered by solver91311)

Solve using the elimination method. Show your work. If the system has no solution or an... (answered by stanbon)

Solve using the elimination method. Show your work. If the system has no solution or an... (answered by richwmiller)

Solve using the elimination method. Show your work. If the system has no solution or an... (answered by neatmath)