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2 years ago

Find the value of x and y.

Mathematics

1 answer:

NISA [10]2 years ago

8 0

Answer:

x = 71 and y = 109

Step-by-step explanation:

x = 180 - 109 = 71

y = 109 vertical angles

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2x-y=3 -x-y=3 what does this equal system of equations

Jet001 [13]

Topic : Linear equations in two variables.

Given :

2x - y = 3 ––– (i)
- x - y = 3 ––– (ii)

Solution :

Now,

(i) – (ii)

$\qquad \sf \: { \dashrightarrow 2x - y - ( - x - y) = 3 - 3}$

$\qquad \sf \: { \dashrightarrow 2x - y + x + y) = 3 - 3}$

$\qquad \sf \: { \dashrightarrow 3x = 0}$

$\qquad \bf \: { \dashrightarrow x = 0}$

Now, substituting the value of x in Eq (i) :

$\qquad \sf \: { \dashrightarrow 2x - y = 3 }$

$\qquad \sf \: { \dashrightarrow 2(0)- y = 3 }$

$\qquad \sf \: { \dashrightarrow 0- y = 3 }$

$\qquad \bf \: { \dashrightarrow y = - 3 }$

Therefore,

The value of x = 0 and y = -3

3 0

2 years ago

Find the equation of the line that passes through (0, -3) and is parallel to

Tresset [83]

Hey there!

$\\$

Answer:

$\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be $\: \sf{d_1} \:$ and the line that is parallel to $\: \sf{d_1} \:$ be $\: \sf{d_2} \:$ .

$\sf{d_2} \:$ passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

$\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}$

$\\$

⇒Subtitute the values :

$\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}$

$\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}$

$\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}$ .

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

$\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.}$

$\implies \sf{y = \bold{\dfrac{7}{6}}x + b}$ $\\$

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line $\: \sf{d_1} \:$ . Now, replace y with -3 and x with 0:

$\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$