Step 1a

To solve the system of equations:
2x + 6y = 7 ---(1)
9x - 5y = 11 ---(2)

Explanation: The provided system of equations is denoted as (1) and (2).

Step 1b

Now use the elimination method:
Multiply equation (1) by 9 and equation (2) by 2 to eliminate the x coefficients:
9(2x + 6y) = 9(7) ⇒ 18x + 54y = 63 ---(3)
2(9x - 5y) = 2(11) ⇒ 18x - 10y = 22 ---(4)
Subtract equation (4) from equation (3) to eliminate the x term
(18x + 54y) - (18x - 10y) = 63 - 22
18x + 54y - 18x + 10y = 63 - 22
64y = 41
Slove for y value: \$y = 41/64 \$

Explanation: Use the elimination method to determine the value of y in the equation and eliminate the x value in the equation.

Step 1c

Substitute the value of y back into equation (1) or (2) to solve for x:
\$ 2x + 6(41/64) = 7\$ (using equation 1)
\$ 2x + 246/64 = 7 \$
\$ 2x = 7 - 246/64 \$
\$ 2x = 448/64 - 246/64 \$
\$ 2x = 202/64 \$
Slove for x value: \$ x = 101/64 \$
So, the solution to the system of equations is \$ x = 101/64 \$ and \$y = 41/64 \$.

Explanation: Replace y with a value in equation (1) or (2) to find x, then simplify for the x value in the equation.

Step 2a

To solve the inequality, let’s simplify the expression first:

\$ 5x - 9y le 8x + 3y - 4 \$

Explanation: Here, simplify the equation.

Step 2b

To isolate the variables on one side, then move the y terms

to the left side and the x terms to the right side:

\$5x - 8x ≤ 3y + 9y - 4\$

Combine like terms

\$-3x ≤ 12y - 4 \$

Explanation: Split variables on each side, then group like terms together for simplification.

Step 2c

Now, let’s isolate the y terms by moving the x terms to the right side:

\$-3x + 4 ≤ 12y\$

Divide both sides of the inequality by 12:

\$ (-3/12)x + 4/12 ≤ y \$

Simplify:

\$ (-1/4)x + 1/3 ≤ y \$

Explanation: Isolate y, simplify, then divide by 12 to yield \$ (-1/4)x + 1/3 ≤ y \$.