Question

possible.
a. \\(6x - 2y = 10\\)
\\(3x - y = 2\\)
b. \\(x - 3y = 1\\)
\\(y = 16 - 2x\\)
8-63. the “≤” symbol represents “less than or equal to,” while the “<” symbol represents “less than.”
a. similarly, translate “≥” and “>.”
b. how can you write an expression that states that 5 is greater than 3?
c. write another expression that states that x is less than or equal to 9

Explanation:

First set of systems of equations (Step-by-Step Format)

Part a:

Step1: Isolate y in second equation

From $3x - y = 2$, rearrange to get $y = 3x - 2$.

Step2: Substitute y into first equation

Substitute $y = 3x - 2$ into $6x - 2y = 10$:
$6x - 2(3x - 2) = 10$
Simplify: $6x - 6x + 4 = 10$ → $4 = 10$

Step3: Analyze the result

$4=10$ is a false statement, so no solution exists.

Part b:

Step1: Substitute y into first equation

Substitute $y = 16 - 2x$ into $x - 3y = 1$:
$x - 3(16 - 2x) = 1$

Step2: Expand and solve for x

$x - 48 + 6x = 1$ → $7x = 49$ → $x = 7$

Step3: Solve for y using x=7

Substitute $x=7$ into $y = 16 - 2x$:
$y = 16 - 2(7) = 16 - 14 = 2$

a. The symbols are direct counterparts to the given ones, with the line under the symbol including equality.
b. Use the "greater than" symbol between the larger and smaller number.
c. Use the "less than or equal to" symbol between x and the specified number.

Answer:

a. No solution
b. $x=7$, $y=2$

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Second set of inequality questions (Answer-Explanation Format)