Solve the linear system by using elimination.
6x+y=39
-2x+y=-17
subtract them
8x = 56
x = 7
sub back into first .....
Thank you!
To solve the linear system using elimination, follow these steps:
Step 1: Multiply one or both equations by a constant if necessary to make the coefficients of one of the variables match.
Let's multiply the second equation by 3 to eliminate y:
-2x + y = -17
(3)(-2x + y) = (3)(-17)
-6x + 3y = -51
Now we have the system of equations:
6x + y = 39
-6x + 3y = -51
Step 2: Add or subtract the equations to eliminate one of the variables.
Add the two equations together:
(6x + y) + (-6x + 3y) = 39 + (-51)
Simplify:
6x - 6x + y + 3y = 39 - 51
4y = -12
Step 3: Solve the resulting equation for the remaining variable.
Divide both sides of the equation by 4:
4y/4 = -12/4
y = -3
Step 4: Substitute the value of the solved variable back into one of the original equations to find the value of the other variable.
Using the first equation:
6x + y = 39
6x + (-3) = 39
6x - 3 = 39
6x = 42
x = 42/6
x = 7
Step 5: Check the solution by substituting the values into the original equations.
Substituting x = 7 and y = -3 into the first equation:
6(7) + (-3) = 39
42 - 3 = 39
39 = 39
Substituting x = 7 and y = -3 into the second equation:
-2(7) + (-3) = -17
-14 - 3 = -17
-17 = -17
Both equations are satisfied, so the solution to the linear system is x = 7 and y = -3.