4x - 6y = 10 y = mx + b In the system of equations, m and b... | SAT Systems of two linear equations in two variables Question, Answer Explained

Question bank / Systems of two linear equations in two variables

Math · AlgebraHard

$4x - 6y = 10$
$y = mx + b$
In the system of equations, $m$ and $b$ are constants. If the system has infinitely many solutions, what is the value of $b$ ?

$-\frac{5}{2}$

$-\frac{5}{3}$

$\frac{2}{3}$

$\frac{5}{3}$

Show answer and explanation

Answer: B

For infinitely many solutions, the two equations must describe the same line. Solve the first equation for $y$ : $-6y = -4x + 10$ , so $y = \frac{2}{3}x - \frac{5}{3}$ . Matching this to $y = mx + b$ gives $m = \frac{2}{3}$ and $b = -\frac{5}{3}$ .

Choice D drops the negative sign when dividing $10$ by $-6$ .

Why the other choices are wrong

A. This divides 10 by -4. To get b, solve for y, which means dividing by -6.
C. 2/3 is the slope m, not the y-intercept b.
D. This drops the sign when dividing by -6. Since -6y = -4x + 10, y = (2/3)x - 5/3.

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