Solve the simultaneous equation.
2x + 3y = 8
3x + 5y = 13

The value of x is 1 while the value of y is 2.

2x + 3y = 8 equation i

3x + 5y = 13 equation ii

We will multiply equation i by the coefficient of x in equation ii and we will multiply equation ii by the coefficient of x in equation ii

Multiply equation i by 3

Multiply equation ii by 2

6x + 9y = 24 iii

6x + 10y = 26 iv

Subtract iii from iv

(10y - 9y) = (26 - 24)

y = 2

Put the value of y into equation i

2x + 3y = 8

2x + 3(2) = 8

2x + 6 = 8

2x = 8 - 6

2x = 2

x = 2/2

x = 1

The value of x is 1

In conclusion, the value of x is 1 and y is 2.

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x = 1; y = 2

Step-by-step explanation:

For this problem, let's take the substitution approach.

2x + 3y = 8

3x + 5y = 13

With the substitution approach, we will simply solve one equation for a variable, and plug that into the other equation to find the values for the variables.

2x +  3y = 8

2x = 8 - 3y

x = 8/2 - 3y/2

3x + 5y = 13

3(8/2 - 3y/2) + 5y = 13

24/2 - 9y/2 + 5y = 13

12 + 1y/2 = 13

1y/2 = 1

y = 2

Now let's plug this value of y into one of the other equations to find the value of x.

2x + 3y = 8

2x + 3(2) = 8

2x + 6 = 8

2x = 2

x = 1

Hence, the solutions for these equations are y = 2 and x = 1.

Cheers.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

thats not a system of equations, that is a solution