9x+6y=3 and 3x-7y=-26 using the substitution method
To solve this system of equations using the substitution method, we need to solve one equation for one variable and then substitute it into the other equation.
Let's solve the first equation, 9x + 6y = 3, for x:
1. Start by isolating x. Subtract 6y from both sides: 9x = 3 - 6y.
2. Now divide both sides by 9: x = (3 - 6y)/9.
We have found the expression for x in terms of y. Let's substitute this into the second equation, 3x - 7y = -26:
3. Replace x with (3 - 6y)/9 in the second equation: 3((3 - 6y)/9) - 7y = -26.
4. Simplify the equation: (9 - 18y)/9 - 7y = -26.
5. Multiply both sides by 9 to eliminate the denominator: 9 - 18y - 63y = -234.
6. Combine like terms: -81y + 9 = -234.
7. Subtract 9 from both sides: -81y = -243.
8. Divide both sides by -81: y = -243/(-81).
9. Simplify the expression: y = 3.
Now that we have the value of y, we can substitute it back into either of the original equations to find the value of x. Let's substitute y = 3 into the first equation, 9x + 6y = 3:
10. Replace y with 3 in the first equation: 9x + 6(3) = 3.
11. Simplify the equation: 9x + 18 = 3.
12. Subtract 18 from both sides: 9x = -15.
13. Divide both sides by 9: x = -15/9.
14. Simplify the expression: x = -5/3.
Therefore, the solution to the system of equations is x = -5/3 and y = 3.