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3 years ago

How many solutions does the following equation have?

1 answer:

7 0

Answer:
Exactly one solution

Explanation:
The first step we need to take to find the answer is to find the value of y.

7(y+3)=5y+8
Expand the parentheses
7y+21=5y+8
Subtract both sides by 21
7y+21-21=5y+8-21
7y=5y-13
Subtract both sides by 5y
7y-5y=5y-13-5y
2y=-13
Divide both sides by 2
2y/2=-13/2
y=-6.5

Now, we plug y back into the original equation.

7(y+3)=5y+8
7(-6.5+3)=5(-6.5)+8
Expand the parentheses
-45.5+21=-32.5+8
-24.5=-24.5

Because both sides of the equation is equal and the equation is true, we can conclude that the equation has one solution.

I hope this helps!

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2 years ago

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2 years ago

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Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}m+4n=8&(1)\\m=n-2&(2)\end{array}\right\\\\\text{substitute (2) to (1):}\\\\n-2+4n=8\qquad\text{add 2 to both sides}\\5n=10\qquad\text{divide both sides by 5}\\n=2\\\\\text{put the value of}\ n\ \text{to (2):}\\\\m=2-2\\m=0$

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3 years ago

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Dmitrij [34]

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2 years ago

I’m confused?????????

QveST [7]

Answer:

The equation of the line is y - 3 = 2.5(x - 2) ⇒ D

Step-by-step explanation:

The rule of the slope of a line is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are two points on the line

The point-slope form of a line is y - y1 = m(x - x1), where

(x1, y1) is a point on the line

From the given figure

∵ The line passes through points (2, 3) and (0, -2)

∴ x1 = 2 and y1 = 3

∴ x2 = 0 and y2 = -2

→ Substitute them in the rule of the slope to find it

∵ m = $\frac{-2-3}{0-2}=\frac{-5}{-2}=2.5$

∴ m = 2.5

→ Substitute the values of m, x1, y1 in the form of the equation above

∵ m = 2.5, x1 = 2, y1 = 3

∵ y - 3 = 2.5(x - 2)

∴ The equation of the line is y - 3 = 2.5(x - 2)

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