The problem asks us to evaluate the expression $2(x^2 - y^3)$ given that $x=3$ and $y=-1$. The second problem asks to solve the following equations simultaneously: $3x - 2y = 10$ $x + 3y = 7$

1. Problem Description

The problem asks us to evaluate the expression $2(x^2 - y^3)$ given that $x=3$ and $y=-1$. The second problem asks to solve the following equations simultaneously:

$3x - 2y = 10$

$x + 3y = 7$

2. Solution Steps

Problem 9:

Substitute $x=3$ and $y=-1$ into the expression $2(x^2 - y^3)$.

$2(x^2 - y^3) = 2((3)^2 - (-1)^3)$

$= 2(9 - (-1))$

$= 2(9 + 1)$

$= 2(10)$

$= 20$

Problem 10:

Solve the system of equations:

$3x - 2y = 10$ (1)

$x + 3y = 7$ (2)

We can solve this system using substitution or elimination. Let's use elimination.

Multiply equation (2) by 3 to eliminate x:

$3(x + 3y) = 3(7)$

$3x + 9y = 21$ (3)

Subtract equation (1) from equation (3):

$(3x + 9y) - (3x - 2y) = 21 - 10$

$3x + 9y - 3x + 2y = 11$

$11y = 11$

$y = 1$

Substitute $y=1$ into equation (2):

$x + 3(1) = 7$

$x + 3 = 7$

$x = 7 - 3$

$x = 4$

So, $x=4$ and $y=1$.

3. Final Answer

Problem 9: C. 20

Problem 10: D. x = 4 and y = 1