Solve each system by substitution

Mathematics

1 answer:

Ira Lisetskai [31]3 years ago

4 0

Answer:

1. 2x + 3y =22

y=4

C. (5,4)

2. y=0

-5x - 2y = -15

B. (3,0)

Step-by-step explanation:

2x+(3)(4)=22

Step 1: Simplify both sides of the equation.

2x+12=22

Step 2: Subtract 12 from both sides.

2x+12−12=22−12

2x=10

Step 3: Divide both sides by 2.

2x/2 = 10/2

x=5

====================================================================

−5x−(2)(0)=−15

Step 1: Simplify both sides of the equation.

−5x−(2)(0)=−15

−5x+0=−15

(−5x)+(0)=−15(Combine Like Terms)

−5x=−15

Step 2: Divide both sides by -5.

−5x/−5 = −15/−5

x=3

You might be interested in

Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D

Ivahew [28]

Check the picture below.

$\bf \textit{Law of Cosines}\\ \quad \\
c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies 
c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}
\\\\\\
\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\
-------------------------------\\\\
\begin{cases}
d=10\\
e=18\\
f=22
\end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D$

$\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D$