Use the substitution method to find solution sets (x,y) for the following systems of equations:
3x-5y=-11
6x+2y=26
3x-5y=-11 (A)
6x=2y=26 (B)
(A)*(2)6x-10y=-22(C)
(B)*(5)30x+10=130(D)
(C)+(D)36x =108
108/36=3
x=3
substitute in (A) or (B) choose easiest
(B)- 18+2y=26 (take 18 from both sides
2y=8
8/2
y=4
so x=3 and y=4
(3,4)
To solve this system of equations using the substitution method, we follow these steps:
Step 1: Solve one of the equations for one variable.
Choose one of the equations to solve for either x or y. Let's solve the first equation, 3x - 5y = -11, for x.
3x - 5y = -11
3x = 5y - 11
x = (5y - 11) / 3
Step 2: Substitute the expression from Step 1 into the other equation.
Take the value of x from Step 1 and substitute it into the second equation, 6x + 2y = 26.
6x + 2y = 26
6((5y - 11) / 3) + 2y = 26
(10y - 22) + 2y = 26
Step 3: Simplify and solve for the variable.
Simplify the equation from Step 2 and solve for the variable y.
10y - 22 + 2y = 26
12y - 22 = 26
12y = 26 + 22
12y = 48
y = 48 / 12
y = 4
Step 4: Substitute the value of y into the expression from Step 1 and solve for the remaining variable.
Substitute the value of y = 4 into the expression x = (5y - 11) / 3 and solve for x.
x = (5(4) - 11) / 3
x = (20 - 11) / 3
x = 9 / 3
x = 3
Step 5: Write the solution as an ordered pair (x, y).
The solution to the system of equations is (x, y) = (3, 4).
Therefore, the solution set for the given system of equations is (3, 4).