9x+6y=3 and 3x-7y=-26 using the substitution method
To solve the system of equations using the substitution method, follow these steps:
1. Start with one of the equations and solve for one variable in terms of the other variable. Let's start with the first equation:
9x + 6y = 3
Solve for x in terms of y: subtract 6y from both sides:
9x = -6y + 3
Divide both sides by 9:
x = (-6y + 3) / 9
2. Substitute the expression for x obtained in step 1 into the other equation. Let's substitute x = (-6y + 3) / 9 into the second equation:
3x - 7y = -26
Replace x with (-6y + 3) / 9:
3((-6y + 3) / 9) - 7y = -26
Simplify the expression:
(-18y + 9) / 9 - 7y = -26
Multiply both sides by 9 to get rid of the denominator:
-18y + 9 - 63y = -234
Combine like terms:
-81y + 9 = -234
Subtract 9 from both sides:
-81y = -243
Divide both sides by -81 to solve for y:
y = -243 / -81 = 3
3. Substitute the value of y found in step 2 back into one of the original equations to solve for x. Let's substitute y = 3 into the first equation:
9x + 6(3) = 3
Solve for x:
9x + 18 = 3
Subtract 18 from both sides:
9x = -15
Divide both sides by 9 to solve for x:
x = -15 / 9 = -5/3
Therefore, the solution to the system of equations is x = -5/3 and y = 3.