substitution
4x + 3y = 3
7x - 9y = 6
from the 1st
3y = 3-4x
or 9y = 9 - 12x
now sub that into the 2nd
7x - (9-12x) = 6
19x = 15
x = 15/19
back into 3y = 3-4x
3y = 3 - 60/19 = -3/19
y = -1/19
To solve this system of equations using the method of substitution, follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation for x:
4x + 3y = 3
4x = 3 - 3y
x = (3 - 3y) / 4
Step 2: Substitute the expression found in Step 1 into the other equation in place of the variable you solved for.
Substitute (3 - 3y) / 4 for x in the second equation:
7((3 - 3y) / 4) - 9y = 6
Step 3: Simplify and solve the resulting equation.
Now, let's solve for y:
Multiplying through by 4 to get rid of the fraction:
7(3 - 3y) - 36y = 24
21 - 21y - 36y = 24
Combining like terms:
-57y = 3
Divide through by -57:
y = -3 / 57
y = -1 / 19
Step 4: Substitute the value found in Step 3 back into one of the original equations to solve for the other variable.
Let's substitute y = -1 / 19 into the first equation:
4x + 3(-1 / 19) = 3
Multiply through by 19 to get rid of the fraction:
76x - 3 = 57
76x = 60
x = 60 / 76
x = 15 / 19
Therefore, the solution to the system of equations is x = 15/19 and y = -1/19.