2x-3y=24
x+6y=18
substitution to solve system of equation. no sulution of infinitely many solutions
Substitute 18 - 6y for x in the first equation, and solve the resulting equation in y
36 - 12y -3y = 24
15 y = 12
y = 4/5.
2x - 12/5 = 24
2x = 26.4
x = 13.2
To solve this system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the second equation for x:
x + 6y = 18
x = 18 - 6y
Step 2: Substitute the expression found in Step 1 into the other equation.
Replace x in the first equation with 18 - 6y:
2(18 - 6y) - 3y = 24
Step 3: Simplify and solve the resulting equation for y.
36 - 12y - 3y = 24
36 - 15y = 24
-15y = 24 - 36
-15y = -12
y = (-12)/(-15)
y = 4/5 or 0.8
Step 4: Substitute the value found for y into one of the original equations to find x.
Let's use the second equation:
x + 6y = 18
x + 6(4/5) = 18
x + 24/5 = 18
x = 18 - 24/5
x = 90/5 - 24/5
x = 66/5 or 13.2
Step 5: Check if the solution satisfies the other equation.
Substitute x = 13.2 and y = 0.8 into the first equation:
2(13.2) - 3(0.8) = 24
26.4 - 2.4 = 24
24 = 24
Since the equation is satisfied, the solution (x, y) = (13.2, 0.8) is the correct solution.
In this case, there is a unique solution to the system of equations, which means there is no infinitely many solutions or no solution situation.