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2 years ago

2. The two equal sides of an isosceles triangle each have a length of 4x + y - 5. The perimeter of the triangle is

Mathematics

1 answer:

Sever21 [200]2 years ago

5 0

9514 1404 393

Answer:

2x +2y -8

Step-by-step explanation:

If the equal sides are 'a' and the third side is 'b', then the perimeter is ...

P = a +a +b = 2a +b

The length of the third side is then ...

b = P -2a . . . . . . subtract 2a from both sides

Substituting the given expressions, we find ...

b = (10x +4y -18) -2(4x +y -5)

b = 10x +4y -18 -8x -2y +10

b = 2x +2y -8 . . . . the length of the third side

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Answer:

$\begin{cases}y=-5x+1\\y=5x-4 \end{cases}$

Step-by-step explanation:

Slope-intercept form of a linear equation:

$\boxed{y=mx+b}$

where:

m is the slope.
b is the y-intercept (where the line crosses the y-axis).

Slope formula

$\boxed{\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}}$

Equation 1

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$\textsf{Let }(x_1,y_1)=(-1, 6)$

$\textsf{Let }(x_2,y_2)=(0, 1)$

Substitute the defined points into the slope formula:

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-6}{0-(-1)}=-5$

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Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

$y=-5x+1$

Equation 2

Define two points on the line:

$\textsf{Let }(x_1,y_1)=(1, 1)$

$\textsf{Let }(x_2,y_2)=(0, -4)$

Substitute the defined points into the slope formula:

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{0-1}=5$

From inspection of the graph, the line crosses the y-axis at y = -4 and so the y-intercept is -4.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

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Conclusion

Therefore, the system of linear equations shown by the graph is:

$\begin{cases}y=-5x+1\\y=5x-4 \end{cases}$

Learn more about systems of linear equations here:

brainly.com/question/28164947

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