Answered

Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the numbers or symbols. 3x+4y=16 -4x-3y=-19



Answer :

wegnerkolmp2741o

Answer:

(4,1)

Step-by-step explanation:

3x+4y=16

-4x-3y=-19

I will solve this system by elimination.  I will eliminate x

Multiply the first equation by 4 and the second equation by 3

4 (3x+4y)=4*16

12x + 16y = 64


3 (-4x-3y)=3*-19

-12x -9y = -57


Add the two modified equations together to eliminate x

12x + 16y = 64

-12x -9y = -57

-----------------------

7y = 7

y=1


We still need to find x

3x+4y = 16

Substitute y=1

3x+4(1) = 16

3x+4=16

Subtract 4 from each side

3x = 16-4

3x =12

Divide each side by 3

3x/3 = 12/3

x=4

Answer:  The required solution is (x, y) = (4, 1).

Step-by-step explanation:  We are given to solve the following system of linear equations :

[tex]3x+4y=16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-4x-3y=-19~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

We will be using the method of Elimination to solve the given system as follows :

Multiplying equation (i) by 4 and equation (ii) by 3, we have

[tex]4(3x+4y)=4\times16\\\\\Rightarrow 12x+16y=64~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

and

[tex]3(-4x-3y)=-19\times3\\\\\Rightarrow -12x-9y=-57~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)[/tex]

Adding equations (iii) and (iv), we get

[tex](12x+16y)+(-12x-9y)=64+(-57)\\\\\Rightarrow 7y=7\\\\\Rightarrow y=\dfrac{7}{7}\\\\\Rightarrow y=1.[/tex]

Substituting the value of y in equation (i), we get

[tex]3x+4\times1=16\\\\\Rightarrow 3x+4=16\\\\\Rightarrow 3x=16-4\\\\\Rightarrow 3x=12\\\\\Rightarrow x=\dfrac{12}{3}\\\\\Rightarrow x=4.[/tex]

Thus, the required solution is (x, y) = (4, 1).