Question

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

Answer 1

Remark

There are two ways to do this. You can graph the equations (which I have included at the end of the question using Desmos) or you can solve it algebraically which in this case is going to be slightly painful.

Algebra

Multiply the first equation by 4 and the second by 3

First Equation

4 [3x + 4y = 16]

12x + 16y = 64             (3)

Second Equation

3 [-4x - 3y = - 19]

- 12x - 9y = - 57           (4)

Add (3) and (4)

12x + 16y = 64

- 12x - 9y = -57           Add

7y = 7                           Divide by 7

y = 1

Solve for x

3x + 4y = 16         Let y = 1

3x + 4(1) = 16

3x + 4 = 16           Subtract 4

3x = 12                 Divide by 3

x = 12/3

x = 4

Answer

(4,1) just as the graph suggests.

Answer 2

Answer:

(4,1)

Step-by-step explanation:

3x + 4y = 16

-4x - 3y = -19

4( 3x + 4y = 16)

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

Distribute

12x + 16y = 64

-12x - 9y = -57

Now subtract both equations

7y = 7

/7 on both sides

y = 1

Substitute y = 1 in one of the equations.

3x + 4y = 16

3x + 4(1) = 16

-4 on both sides

3x = 12

/3 on both sides

x = 4

Answer:

x = 4

y = 1