Question

solve the following system of linear equations using method of substitution n : 3x=2y+1 and 5x=3y+3​

Answer 1

Answer:

The solution to the given system of linear equations is x = 3 and y = 4.

Step-by-step explanation:

To solve the system of linear equations using the method of substitution, we'll solve one equation for one variable and substitute it into the other equation. Let's start with the first equation:

Equation 1: 3x = 2y + 1

We'll solve Equation 1 for x:

3x = 2y + 1

$x = \frac{2y +1}{3}$

We'll now enter this x value in the second equation:

Equation 2: 5x = 3y + 3

Substituting the value of x:

$\frac{5(2y +1)}{3} = 3y +3$

Next, we'll simplify the equation:

$\frac{10y + 5}{3} = 3y + 3$

To eliminate the fraction, we can multiply both sides of the equation by 3:

10y + 5 = 9y + 9

Now, we'll isolate the variable y by moving all terms involving y to one side:

10y - 9y = 9 - 5

y = 4

We have found the value of y, which is y = 4.

Now, we'll substitute this value back into Equation 1 to find the value of x:

3x = 2y + 1

3x = 2(4) + 1

3x = 8 + 1

3x = 9

x = 3

We have found the values of both x and y, which are x = 3 and y = 4.

Therefore, the solution to the given system of linear equations is x = 3 and y = 4.

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