Question

What is the value of the x variable in the solution to the following system of equations? (5 points)

4x − 3y = 3
5x − 4y = 3

x can be any number as there are infinitely many solutions to this system
There is no x value as there is no solution to this system
−3
3

Answer 1

x=3

Explanation:

to understand this

you need to know about:

• system of linear equation
• PEMDAS
• solving system of linear equation using substitution method

given:

4x − 3y = 3

5x − 4y = 3

let's justify how many solutions the system of linear equation has

a system of linear equation has one solution when

• 
  `( a_(1) )/(a_2) ≠ (b_1)/(b_2)`

`(4 )/(5) ≠ ( - 3)/( - 4)`

therefore

this system of linear equation has only one solution

let's figure out x using substitution method:

4x − 3y = 3.......1

5x − 4y = 3.......2

get from 1st equation

`4x - 3y = 3 \\ - 3y= - 4x + 3 \\ y = ( - 4x + 3)/( - 3 ) \\ y = (4)/(3) x - 1`

`subsitute \: got \: volue \: of \: y \: into \: 2nd \: equation`

`5x - 4( (4)/(3) x - 1) = 3 \\ 5x - (16)/(3) x + 4 = 3 \\ 5x - (16)/(3) x = - 1 \\ (15x - 16x)/(3) = - 1 \\ - x = - 3 \\ \huge \therefore \: x = 3`

Answer 2

• D. 3

Explanation:

Given system:

• 4x − 3y = 3
• 5x − 4y = 3

Solve for x by elimination method:

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

• 4(4x - 3y) = 4(3) ⇒ 16x - 12y = 12
• 3(5x - 4y) = 3(3) ⇒ 15x - 12y = 9

Subtract the second equation:

• 16x - 12y - 15x + 12y = 12 - 9
• x = 3

Correct option is D