Question

homework
part i: solve each system of equations

1. **

$x + y = 29$
$x + 2y = 12$

1. **which of the following represents the y value to

the solution of the system below?
$3x - 5y = 19$
$-3x - y = -7$
a) $y = 2$
b) $y = -2$
c) $y = 3$
d) $y = -3$

1. **

$\

$$\begin{cases}3x + 6y = 10\\\\-4x + 6y = 3\\end{cases}$$

$
4.
$4x - 5y = 20$
$6x + 5y = -10$

Explanation:

Problem 1

Step1: Subtract first equation from second

$(x + 2y) - (x + y) = 12 - 29$

Step2: Simplify to solve for $y$

$y = -17$

Step3: Substitute $y$ into first equation

$x + (-17) = 29$

Step4: Solve for $x$

$x = 29 + 17 = 46$

Problem 2

Step1: Add the two equations

$(3x - 5y) + (-3x - y) = 19 + (-7)$

Step2: Simplify to solve for $y$

$-6y = 12 \implies y = \frac{12}{-6} = -2$

Problem 3

Step1: Subtract second equation from first

$(3x + 6y) - (-4x + 6y) = 10 - 3$

Step2: Simplify to solve for $x$

$7x = 7 \implies x = 1$

Step3: Substitute $x$ into first equation

$3(1) + 6y = 10$

Step4: Solve for $y$

$6y = 10 - 3 = 7 \implies y = \frac{7}{6}$

Problem 4

Step1: Add the two equations

$(4x - 5y) + (6x + 5y) = 20 + (-10)$

Step2: Simplify to solve for $x$

$10x = 10 \implies x = 1$

Step3: Substitute $x$ into first equation

$4(1) - 5y = 20$

Step4: Solve for $y$

$-5y = 20 - 4 = 16 \implies y = -\frac{16}{5}$

Answer:

1. $x=46$, $y=-17$
2. b) $y = -2$
3. $x=1$, $y=\frac{7}{6}$
4. $x=1$, $y=-\frac{16}{5}$