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

Answer:

• D. 3

Step-by-step 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

Answer 2

Answer:

x=3

Step-by-step 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

• $\frac{ a_{1} }{a_2} ≠ \frac{b_1}{b_2}$

$\frac{4 }{5} ≠ \frac{ - 3}{ - 4}$

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

$4x - 3y = 3 \\ - 3y= - 4x + 3 \\ y = \frac{ - 4x + 3}{ - 3 } \\ y = \frac{4}{3} x - 1$

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

$5x - 4( \frac{4}{3} x - 1) = 3 \\ 5x - \frac{16}{3} x + 4 = 3 \\ 5x - \frac{16}{3} x = - 1 \\ \frac{15x - 16x}{3} = - 1 \\ - x = - 3 \\ \huge \therefore \: x = 3$