Question

for each ordered pair, determine whether it is a solution to the system of equations.
\

$$\begin{cases} y = 2x + 1 \\\\ -5x + 3y = 8 \\end{cases}$$

(a) is (0, 1) a solution?
\bigcirc yes \quad \bigcirc no
(b) is (-7, -9) a solution?
\bigcirc yes \quad \bigcirc no
(c) is (5, 11) a solution?
\bigcirc yes \quad \bigcirc no
(d) is (3, -2) a solution?
\bigcirc yes \quad \bigcirc no

Explanation:

Part (a)

Step1: Check first equation \( y = 2x + 1 \)

Substitute \( x = 0 \), \( y = 1 \): \( 1 = 2(0) + 1 \) → \( 1 = 1 \), holds.

Step2: Check second equation \( -5x + 3y = 8 \)

Substitute \( x = 0 \), \( y = 1 \): \( -5(0) + 3(1) = 3
eq 8 \), does not hold.

Step1: Check first equation \( y = 2x + 1 \)

Substitute \( x = -7 \), \( y = -9 \): \( -9 = 2(-7) + 1 \) → \( -9 = -13 \), does not hold.

Step1: Check first equation \( y = 2x + 1 \)

Substitute \( x = 5 \), \( y = 11 \): \( 11 = 2(5) + 1 \) → \( 11 = 11 \), holds.

Step2: Check second equation \( -5x + 3y = 8 \)

Substitute \( x = 5 \), \( y = 11 \): \( -5(5) + 3(11) = -25 + 33 = 8 \), holds.

Answer:

No

Part (b)