2x - y = -1 And 3x + 4y = 26

Question

Math is very hard for me especially when it come down to elimination and subsitution

Answer 1

Hi Marah,

 

Let's see if we can get you some help. To solve this System of Equations by Substitution, start by solving for any variable in either equation. Personally, I will try to choose to solve for any variable with a coefficient of 1 (or negative 1), so I will solve for y in the first equation.

 

2x - y = -1

 

Subtract 2x from both sides of the equation.

 

-y = -2x -1

 

Multiply both sides of the equation by -1.

 

-1( -y = -2x -1)

 

y = 2x +1 Keep up with this! It's very important! 

If y EQUALS 2x + 1 then they are equivalent and each my replace the other. We're gonna do that.

 

Now, use the second equation:

 

3x + 4y = 26

 

Replace the y here with the expression that y is equivalent to from the first equation.

 

3x + 4(2x + 1) = 26

 

Distribute the 4.

 

3x + 8x + 4 = 26

 

Combine like terms.

 

11x + 4 = 26

 

Subtract 4 from both sides of the equation.

 

11x = 22

 

Divide both sides of the equation by 11 to isolate the x.

 

x = 2

 

Great! We're almost there! 

 

Now go back to that equation that I said was important before.

 

y= 2x + 1

Since x EQUALS 2, they are equivalent and each may replace the other. So now, replace the x in this important equation with 2.

 

y= 2 (2) + 1

y= 4 + 1

y= 5

 

Now put it all together: if x = 2 and y = 5, then the solution to this system of intersecting linear equations is the point, (2,5), where they intersect.

 

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To solve with Elimination:

 

Write the equations under one another, like this:

 

     2x -  y   = -1

+   3x + 4y = 26

 

Ideally, we would like for one of the variables to be eliminated when we add vertically (straight down). But if we add them as they are this does not happen. We must manipulate one of the equations so that it will happen. Again, you can try to eliminate either x or y. I always look for a term that has a coefficient of 1 (or negative 1). So, let's use that y from the first equation again.

 

If the coefficient of the y in the other equation is POSITIVE 4, then I need the coefficient from the first equation to be its opposite, NEGATIVE 4.  To do this, simply multiply the first equation by 4, this will create MAGIC!

 

     4( 2x - y  = -1)

+  3x + 4y = 26

 

Be certain to Distribute across the entire first equation, so multiply all three terms by 4.

 

   8x - 4y = -4

+ 3x + 4y = 26

 

Now add straight down (vertically).  The y term will be eliminated.

 

11x = 22

 

Divide both sides of the equation by 11.

 

x = 2

 

Almost there! Now, substitute the 2 in for x in either of the original equations. Either one will work. I'm gonna use the second equation.

 

3x + 4y = 26

 

3(2) + 4y = 26

 

6 + 4y = 26

 

Subtract 6 from both sides of the equation.

 

4y = 20

 

Divide both sides of the equation by 4.

 

y = 5

 

That's it! There it is again. Put it all together. If x = 2 and y = 5, then the solution is the ordered pair, (2,5).

 

Good luck!

 

 

 

Answer 2

Marah, I promise this is easier than you think!

 

If we multiply an equation by anything, the graph stays exactly the same.

 

What we want is for one of the variables to have opposites, like -5x and 5x, because we want them to cancel out when we add the equations together.

 

2x - y = -1

3x + 4y = 26

 

Looking at this, we could multiply equation 1 by -3 and the 2nd by 2 so we have -6x and 6x. What looks easier, though is multiplying the first by 4, becauze that will give us -4y and 4y.

 

8x - 4y = -4

3x + 4y = 26

 

Adding the two together, we get 11x = 22, so x = 2.

 

Now we can take that 2 and solve for y using either equation.

 

2(2) - y = -1

4 - y = -1

y = 5

 

Sooooo, our solution is (2,5).

 

Hope this helps!

Answer 3

For the two formulae the key is as you mention substitution.

 

Taking the first equation 2x - y = -1.  This can be re-ordered as follows: y = 2x + 1.  This can then be placed into the second equation as follows:

 

3x + 4(2x + 1) = 26 => 3x + 8x + 4 = 26 => 11x = 22 => x = 2.  Placing this into the above y = 2x + 1 you get to:

 

y = 2(2) + 1 => y = 5

 

Therefore x = 2 and y = 5