9x+6y=3 and 3x-7y=-26 using the substitution method
9x+6y=3 (1)
3x-7y=-26 (2)
using substitution method in (1) we get
9x+6y=3
dividing by 3 both side we get
3x+2y=1
taking 2y to the other side (here 2y in + so when we change its side it will be -)
3x=1-2y
(here 3 is multiply with x so when it goes other side sign will change in divide)
x=(1-2y)/3 (3)
3x-7y=-26 (2)
putting the value of x in (2) from (3)
3*(1-2y)/3-7y=-26
(3 will cancel by 3)
1-2y-7y=-26
1-9y=-26
taking constant no. Same side
-9y=-26-1
-9y=-27
(both sides minus sign will cancel by each other)
9y=27
y=27/9
y=3
putting the value of y in (3)
x=(1-3*2)/3
x=(1-6)/3
x=-5/3
(u can check ur ans by putting the value of 'x' and 'y' in (1) and (2))
To solve the system of equations 9x + 6y = 3 and 3x - 7y = -26 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 first equation, 9x + 6y = 3, for x:
9x = 3 - 6y
x = (3 - 6y) / 9
Step 2: Substitute the expression for x from the first equation into the second equation.
Replace x in the second equation, 3x - 7y = -26, with the expression we found for x in Step 1:
3[(3 - 6y) / 9] - 7y = -26
Step 3: Simplify and solve for y.
To simplify, multiply both sides of the equation by 9 to eliminate the fraction:
3(3 - 6y) - 63y = -234
9 - 18y - 63y = -234
-81y = -243
y = (-243) / (-81)
y = 3
Step 4: Substitute the value of y back into one of the original equations to solve for x.
Let's use the first equation, 9x + 6y = 3:
9x + 6(3) = 3
9x + 18 = 3
9x = 3 - 18
9x = -15
x = (-15) / 9
x = -5/3
Therefore, the solution to the system of equations 9x + 6y = 3 and 3x - 7y = -26 is x = -5/3 and y = 3.