Question

3x − 2y = a ;
−15x + 10y = −7
In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a?

• A. $\frac{7}{5}$
• B. $\frac{-5}{7}$
• C. $\frac{4}{7}$
• D. $\frac{-7}{4}$

Answer 1

The correct option is A $\frac{7}{5}$

For a system of linear equations to have infinite solutions , the ratio of the coefficients of x, y and constants must be $\frac{a1}{a2}=\frac{b1}{b2}=\frac{c1}{c2}$.
To simplify the equations , multiply the first equation by -5 , which gives :
-15x + 10y = -5a
-15x + 10y = -7
From here its is evident that $\frac{a1}{a2}=\frac{b1}{b2}=\frac{c1}{c2}=1$.Therefore $-5a=-7$ or $a=\frac{7}{5}$. Hence the answer is A