Question

Which of the following pair of equations satisfies y = x?

• A. $4x=16,5y+3=17$
• B. $4x+8=18$ and $4y=20$
• C. $3x–3=19,4y+9=17$
• D. $6x+4=10$ and $3y+2=5$

Answer 1

The correct option is D $6x+4=10$ and $3y+2=5$

Consider the equations: 4x = 16 and 5y + 3 = 17
$\Rightarrow x=\frac{16}{4}$ and 5y = 14
$\Rightarrow x=4$ and $y=\frac{14}{5}$
$\Rightarrow y\ne x$
Consider the equations:
4x + 8 = 18 and 4y = 20
$\Rightarrow 4x=10$ and $y=\frac{20}{4}$
$\Rightarrow x=\frac{5}{2}$ and y = 5
$\Rightarrow y\ne x$
Consider the equations:
3x – 3 = 19 and 4y + 9 = 17
$\Rightarrow 3x=22$ and $4y=8$
$\Rightarrow x=\frac{22}{3}$ and y =2
$\Rightarrow y\ne x$
Consider the equations:
6x + 4 = 10 and 3y + 2 = 5
$\Rightarrow 6x=6$ and 3y = 3
$\Rightarrow x=1$ and y = 1
$\Rightarrow y=x$
Hence, the correct answer is option (d).