All categories

3 years ago

{-2x+y=0 5x+3y=-11 Solve the substitution

1 answer:

7 0

$\bf \begin{cases} -2x+y=0\\ \boxed{y} = 2x\\[-0.5em] \hrulefill\\ 5x+3y=-11 \end{cases}\qquad \qquad \implies \stackrel{\textit{substituting on the 2nd equation}}{5x+3\left( \boxed{2x} \right)=-11} \\\\\\ 5x+6x=-11\implies 11x=-11\implies x = \cfrac{-11}{11}\implies \blacktriangleright x = -1 \blacktriangleleft \\\\\\ \stackrel{\textit{we know that}}{y = 2x}\implies \blacktriangleright y = -2 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-1~~,~~-2)~\hfill$

You might be interested in

Divide 30 in a ratio of 3:2

Sergeeva-Olga [200]

$Other\ method:\\\\x;y-searches\\\\ \left\{\begin{array}{ccc}x+y=30&|subtract\ y\ from\ both\ sides\\x:y=3:2\end{array}\right\\\left\{\begin{array}{ccc}x=30-y&(1)\\\frac{x}{y}=\frac{3}{2}&(2)\end{array}\right\\\\subtitute\ (1)\ to\ (2):\\\\\frac{30-y}{y}=\frac{3}{2}\ \ \ \ |cross\ multiply\\\\(3)(y)=(2)(30-y)\\3y=60-2y\ \ \ \ |add\ 2y\ to\ both\ sides\\5y=60\ \ \ \ |divide\ both\ sides\ by\ 5\\\boxed{y=12}$

$Put\ the\ value\ of\ y\ to\ (1):\\x=30-12\\\boxed{x=18}\\\\Answer:\boxed{\left\{\begin{array}{ccc}x=18\\y=12\end{array}\right\to18:12}$

4 0

3 years ago

Read 2 more answers

Indigo Company had cash sales of $78,120 (including taxes) for the month of June. Sales are subject to 8.5% sales tax. how to re

s2008m [1.1K]

Answer:

Step-by-step explanation:

Sales revenue x (100%+sales tax rate) = total sales including tax

sales revenue x 1.085 (100% + 8.5%) = 78120

sales revenue = 78120/1.085

sales revenue = 72000

total sales including tax - sales revenue = sales tax

78120 = 72000 = 6120

Journal entry:

cash. 78120

Sales revenue. 72000

Sales tax payable. 6120

4 0

2 years ago

What is the y-intercept of a line that has a slope of 1/4 and passes through point (8,3)

exis [7]

Answer:

Step-by-step explanation:

Y-y1=m(x-x1)

Y- 3= 1/4(x- 8)

Y-3= 1/4x- 2

Y= 1/4x+1

Y intersept= 1

6 0

3 years ago

A factory produced 150 tons of steel in one year. The next year, the output increased to 180 tons. What is the percentage increa

nirvana33 [79]

The amount of increase is (180 - 150) = 30 tons.

The increase as a part of the original amount is 30/150 = 0.2

To change a decimal into a percent,
move the decimal point 2 places that way ===> .

0.2 = 20%

4 0

3 years ago

0what is the perimeter of a rhombus-shaped sign with a 35-cm side?

Romashka [77]

Rhombus is 4 sided figure with 4 sides same lgenth

preimiter=4 times side
35 times 4=140

perimiter=140 cm

8 0

3 years ago

Read 2 more answers