Question

Solve the given system of linear equations.

2x + 3y = 3 --------(i)
4x + 2y = 5 --------(ii)

Answer 1

To solve the given system of linear equations 2x + 3y = 3 and 4x + 2y = 5, we can use the method of substitution or elimination. In this case, let's solve using the method of elimination: Multiply equation (i) by 2 and equation (ii) by 3 to eliminate the x variable. Subtract equation (i) from equation (ii) to eliminate the y variable. Divide both sides of the equation by 8 to solve for x. Substitute the value of x into either equation to find the value of y. The solution to the system of linear equations is x = 1.125 and y = -0.375.

Step-by-step explanation:

To solve the given system of linear equations 2x + 3y = 3 and 4x + 2y = 5, we can use the method of substitution or elimination.

Method of Substitution:

1. Solve one of the equations for one variable in terms of the other variable.
2. Substitute the expression found in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found in step 3 back into either equation to find the value of the other variable.
5. The solution is the values of both variables that satisfy both equations.

Method of Elimination:

1. Multiply one or both of the equations by a constant to make the coefficients of one of the variables equal or opposite in both equations.
2. Add or subtract the two equations to eliminate one of the variables.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found in step 3 back into either equation to find the value of the other variable.
5. The solution is the values of both variables that satisfy both equations.

In this case, let's solve using the method of elimination:

1. Multiply equation (i) by 2 and equation (ii) by 3 to eliminate the x variable. This gives us 4x + 6y = 6 and 12x + 6y = 15.
2. Subtract equation (i) from equation (ii) to eliminate the y variable. This gives us 8x = 9.
3. Divide both sides of the equation by 8 to solve for x. x = 9/8 or 1.125.
4. Substitute the value of x into either equation to find the value of y. Using equation (i), we have 2(1.125) + 3y = 3. Solving for y gives us y = -0.375 or -3/8.
5. The solution to the system of linear equations is x = 1.125 and y = -0.375.