To solve this system of equations, you can use the substitution method or the elimination method.
Using the substitution method:
1. Solve one equation for one variable in terms of the other variable.
From equation 1, solve for y:
y = (2/3)x + 6
2. Substitute the expression for y in terms of x into the other equation.
Substitute (2/3)x + 6 for y in equation 2:
3((2/3)x + 6) + 6x - 18 = 0
3. Simplify and solve for x:
2x + 18 + 6x - 18 = 0
8x = 0
x = 0
4. Substitute the value of x back into one of the original equations and solve for y:
Using equation 1:
y = (2/3)(0) + 6
y = 0 + 6
y = 6
Therefore, the solution to the system of equations is x = 0 and y = 6.
Using the elimination method:
1. Multiply equation 1 by 3 to eliminate the fractions:
3y = 2x + 18
2. Rewrite equation 2 as:
6x - 18 = -3y
3. Add the two equations together to eliminate the y-variable:
3y + 6x - 18 + 6x - 18 = 0
6x + 6x - 3y + 3y - 36 = 0
12x - 36 = 0
4. Solve for x:
12x = 36
x = 36/12
x = 3
5. Substitute the value of x back into one of the original equations and solve for y:
Using equation 1:
y = (2/3)(3) + 6
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is x = 3 and y = 8.
solve
y=2/3x+6
3y+6x-18=0
1 answer
1 answer