-3x + 4y =76x + 5y =57

Question

i have no idea what im doing. i missed a day and now my teacher wont tell me how to do this

Answer 1

Keyana,

 

You have two unknowns, x and y, so you need two equations.  You actually have three here to choose from.

 

Here are the three equations:

1.  -3x + 4y = 57

2.  76x +5y =57

3.  -3x + 4y = 76x + 5y 

 

Equation 3 can be changed by subtracting -3x+4y from both sides, giving 79x + y = 0.

 

Since there are three equations, it's possible there is no solution if two of the equations are not dependent. If we end up with a contradiction, then that would be the case.  But in this case there is a solution.  

 

Since 79x + y = 0,   y = -79x.   Now use this result to substitute for y into equation 1. giving 

 

-3x + 4(-79x) = 57,   or  -319x = 57,  or x = -57/319

 

Now y = -79x,  and so y = 57*79/319 = 4503/319

 

By the way, here is a web site that will help you verify your answers to questions like this:

 

http://www.numberempire.com/equationsolver.php

 

Answer 2

I think this is what Keyana meant:

 

-3x + 4y = 76

x + 5y = 57

 

If you solve the second equation for x = 57 - 5y,

you can substitute 57 - 5y for x in the first equation:

-3(57 - 5y) + 4y = 76 and solve for y:

Distribute:

-171 + 15y + 4y = 76

Add 171 to both sides and collect like terms:

19y = 247

Divide both sides by 19:

y = 13

 

Now substitute 13 for y in x = 57 - 5y and solve for x:

x = 57 - 5(13)

x = 57 - 65

x = -8

 

So the solution to the given system of equations is (-8,13).

 

check:

-3(-8) + 4(13) =? 76

24 + 52 = 76 √

 

(-8) + 5(13) =? 57

-8 + 65 = 57 √

 

That was solving by the technique known as Substitution.

 

Here's how you might solve by using Elimination:

 

-3x + 4y = 76
x + 5y = 57

 

Multiply the second equation by 3 so that the x terms are opposites:

 

-3x + 4y = 76
3x + 15y = 171

 

Now add the two equations; i.e., add the left sides together and add the right sides together:

 

0 + 19y = 247

Divide both sides by 19:

y = 13

 

At this point you could just substitute 13 for y into either original equation and solve for x. But let's go back and try to eliminate y from the original equations:

 

-3x + 4y = 76
x + 5y = 57

 

We want the y terms to be opposites, so let's multiply the first equation by -5 and the second by 4:

 

-3(-5)x + 4(-5)y = 76(-5)
(4)x + 5(4)y = 57(4)

 

15x - 20y = -380

 4x + 20y = 228

 

Add the two equations:

 

19x + 0 = -152

 

Divide both sides by 19:

 

x = -8

 

So with Elimination we found the solution to be (-8, 13).

Answer 3

The approach in solving this or similar system is that you have to substitute one of the coefficients with another, viz:

if you have a simpler system, such as:

x + 2y = 3

2y-x = 1

 

To find out the solution, you would re-write it as:

x = 3 - 2y and replace the x in the other equation with that:

2y - x = 2y - (3 - 2y) = 2y - 3 + 2y = 4y - 3

so now you have:

 

4y - 3 = 1 => 4y = 1+3 = 4 => y = 1 

Now, you replace y with 1 in the other equation: x + 2x1 = 3 => x = 3 - 2 = 1

so, x = 1, y = 1

Answer 4

Hi Keyana;

-3x + 4y =76x + 5y =57

I think this is...

-3x + 4y =76

x + 5y =57

 

If it is not, please let me know...

 

Let's begin with the second equation...

x + 5y =57

Let's note the fact that in the first equation, the coefficient of x is -3.

So, let's multiply both sides of this equation by -3...

-3(x + 5y) =57(-3)

-3x-15y=-171

 

Let's subtract the first equation from the second equation...

-3x-15y=-171

-(-3x + 4y =76)

(-3x)-(-3x)=(-3x)+(3x)=0

-15y-(4y)=-19y

-171-76=-247

0-19y=-247

-19y=-247

Let's divide both sides by -19...

y=13

 

Let's return to the original equations...

-3x + 4y =76

Let's plug-in y=13 to establish x...

(-3x)+[(4)(13)]=76

-3x+52=76

Let's subtract 52 from both sides...

-3x=24

Let's divide both sides by -3...

x=-8

Let's plug-in x=-8 and y=13 into the other equation to verify...

x + 5y =57

-8+[(5)(13)]=57

-8+65=57

57=57

(-8,13)

PLEASE LET ME KNOW IF I MISUNDERSTOOD.