Question 63·200 Super-Hard SAT Math Questions·Algebra

0 / 200 Questions completed

11kx - 6my = 99.5

5kx + 9my = 108.75

In the given system of equations, $k$ and $m$ are constants. The system has a solution of $(-4, y)$ . Which choice is the value of $k$ ?

In a linear system where the same products appear in both equations, treat each product as one temporary unknown. Use a Desmos list regression to find the product involving the constant you need, then use the given coordinate to separate them. Finding $kx$ is not the same as finding $k$ . Keep the sign of the given coordinate when you finish.

Hints

Hint 1
The products $kx$ and $my$ each appear in both equations. Treat each whole product as one unknown: call them $a=kx$ and $b=my$ . Which of those will help you find $k$ ?
Hint 2
A list regression can match the two left sides to the two right sides at once. In Desmos, use $\sim$ between the lists, then read the value of $a$ under PARAMETERS.
Hint 3
In an ordered pair, the first coordinate is $x$ . Use $x=-4$ in $a=kx$ after you find $a$ . Keep the negative sign when you solve for $k$ .

Step-by-step

Solve for the repeated product in Desmos
Step 1
Rewrite the system using repeated products
Let $a=kx$ and $b=my$ . Each equation now uses the same two unknowns, so rewrite the system as $11a-6b=99.5,\qquad 5a+9b=108.75$ .
Step 2
Find the product $kx$
Type $[11a-6b,5a+9b]\sim[99.5,108.75]$ in Desmos. The $\sim$ tells Desmos to match the lists entry by entry. Under PARAMETERS, it reports $a=12$ . That is $kx$ , not $k$ .
Step 3
Use the given $x$ -coordinate
The first coordinate of $(-4,y)$ says $x=-4$ . Since $a=kx$ and Desmos found $a=12$ , substitute both values: $12=(-4)k$ . You don't need to find $y$ to get the constant $k$ .
Step 4
Solve for $k$
Type $-4k\sim12$ in Desmos. It reports $k=-3$ under PARAMETERS. The constant is negative because its product with $x=-4$ is positive. So the value of $k$ is $-3$ . Choice C.

Question 63·200 Super-Hard SAT Math Questions·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this