Introduction:

We are given two equations 2x 3y-10=0 and y=5-3/2x. We need to find the values of x and y that satisfy both the equations.

Method:

The given pair of equations can be solved using the substitution method. We will solve one equation for one variable and substitute that value into the second equation to find the value of the other variable.

Solution:

We are given the equations:
2x + 3y = 10 (Equation 1)
y = 5 - (3/2)x (Equation 2)

Step 1: Solve Equation 2 for y:
y = 5 - (3/2)x
Multiply both sides by 2 to eliminate the fraction:
2y = 10 - 3x
Add 3x to both sides:
3x + 2y = 10 (Equation 3)

Step 2: Substitute Equation 3 into Equation 1 for y:
2x + 3y = 10
3x + 2y = 10 (Equation 3)
Substitute 3x + 2y for 10 in Equation 1:
2x + 3(3x + 2y) = 10
2x + 9x + 6y = 10
Simplify:
11x + 6y = 10 (Equation 4)

Step 3: Solve Equation 4 for y:
11x + 6y = 10
Subtract 11x from both sides:
6y = -11x + 10
Divide both sides by 6:
y = (-11/6)x + (5/3) (Equation 5)

Step 4: Compare Equations 2 and 5:
Equation 2: y = 5 - (3/2)x
Equation 5: y = (-11/6)x + (5/3)
Since both equations are equal to y, we can set them equal to each other:
5 - (3/2)x = (-11/6)x + (5/3)
Simplify:
15/2 - 3x/2 = -11x/6 + 5/3
Multiply both sides by 6 to eliminate the fractions:
45 - 9x = -22x + 10
Add 22x to both sides:
45 + 13x = 10
Subtract 45 from both sides:
13x = -35
Divide both sides by 13:
x = -35/13

Step 5: Find the value of y using Equation 2:
y = 5 - (3/2)x
y = 5 - (3/2)(-35/13)
y = 5 + (105/26)
y = (155/26)

Therefore, the solution of the given pair of equations is x = -35/13 and y = 155/26.