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.

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step-by-step explanation: