Question

find the x- and y-intercepts. (lesson 5-2)

1. $6x - 2y = 12$ 46. $-3y + x = 15$ 47. $4y - 40 = -5x$

tell whether each ordered pair is a solution of the given system. (lesson 6-1)

1. $(3, 0)$; $\

$$\begin{cases}2x - y = -6 \\\\ x + y = 3\\end{cases}$$

$ 49. $(-1, 4)$; $\

$$\begin{cases}y - 2x = 6 \\\\ x + 4y = 15\\end{cases}$$

$ 50. $(5, 6)$; $\

$$\begin{cases}\\frac{1}{3}y + x = 7 \\\\ 2x = 12\\end{cases}$$

$
s of equations and inequalities

Explanation:

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Problems 45-47: Find x- and y-intercepts

For x-intercept: Set $y=0$, solve for $x$.
For y-intercept: Set $x=0$, solve for $y$.

Problem 45: $6x - 2y = 12$

Step1: Find x-intercept ($y=0$)

$6x - 2(0) = 12$
$6x = 12$
$x = 2$

Step2: Find y-intercept ($x=0$)

$6(0) - 2y = 12$
$-2y = 12$
$y = -6$

Problem 46: $-3y + x = 15$

Step1: Find x-intercept ($y=0$)

$-3(0) + x = 15$
$x = 15$

Step2: Find y-intercept ($x=0$)

$-3y + 0 = 15$
$-3y = 15$
$y = -5$

Problem 47: $4y - 40 = -5x$ (rewrite as $5x + 4y = 40$)

Step1: Find x-intercept ($y=0$)

$5x + 4(0) = 40$
$5x = 40$
$x = 8$

Step2: Find y-intercept ($x=0$)

$5(0) + 4y = 40$
$4y = 40$
$y = 10$

Substitute $x,y$ from the pair into both equations. If both are true, it is a solution.

Problem 48: $(3,0)$;

$$\begin{cases}2x - y = -6 \\ x + y = 3\end{cases}$$

Step1: Substitute into first equation

$2(3) - 0 = 6
eq -6$ (False)

Step2: Substitute into second equation

$3 + 0 = 3$ (True)
Since one equation is false, the pair is not a solution.

Problem 49: $(-1,4)$;

$$\begin{cases}y - 2x = 6 \\ x + 4y = 15\end{cases}$$

Step1: Substitute into first equation

$4 - 2(-1) = 4 + 2 = 6$ (True)

Step2: Substitute into second equation

$-1 + 4(4) = -1 + 16 = 15$ (True)
Both equations are true, so the pair is a solution.

Problem 50: $(5,6)$;

$$\begin{cases}\frac{1}{3}y + x = 7 \\ 2x = 12\end{cases}$$

Step1: Substitute into first equation

$\frac{1}{3}(6) + 5 = 2 + 5 = 7$ (True)

Step2: Substitute into second equation

$2(5) = 10
eq 12$ (False)
Since one equation is false, the pair is not a solution.

Answer:

(45-47):

1. x-intercept: $(2, 0)$; y-intercept: $(0, -6)$
2. x-intercept: $(15, 0)$; y-intercept: $(0, -5)$
3. x-intercept: $(8, 0)$; y-intercept: $(0, 10)$

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Problems 48-50: Check if ordered pair is a solution