Question

7x + 3 y = 15;
14x + 24y = 10
Which ordered pair (x, y) satisfies the system of equations above?

• A. $(\frac{-55}{21},\frac{-10}{9})$
• B. $(\frac{55}{21},\frac{-10}{9})$
• C. $(\frac{40}{21},\frac{5}{9})$
• D. $(\frac{40}{21},\frac{-5}{9})$

Answer 1

The correct option is B $(\frac{55}{21},\frac{-10}{9})$

7x + 3 y = 15 ..... (i)
14x + 24y = 10 ..... (ii)
Consider equation (i)
[ Fix one variable on LHS and shift everything on the other side ]
$\Rightarrow 7x=15-3y$
$\Rightarrow \frac{(15-3y)}{7}$ ...... (iii)
Put the value of x in equation (ii) and simplify the equation
$14\left[\frac{15-3y}{7}\right]+24y=10$
$\Rightarrow 2[15-3y]+24y=10$
$\Rightarrow 30-6y+24y=10$
$\Rightarrow 18y=-20$
$\Rightarrow y=\frac{-20}{18}=\frac{-10}{9}$
Clearly you can eliminate answer option (C) and (D)
Use the value in (iii)
$x=\frac{[15-3\left[\frac{-10}{9}\right]]}{7}$
$=\frac{[15+\frac{10}{3}]}{7}$
$=\frac{55}{21}$
Hence, the correct answer is (B).