Solve the given system by the substitution
method. 2x+y=6, 5x-2y=6
y=6-2x, so
5x - 2(6-2x) = 6
solve for x, then figure y
To solve the given system using the substitution method, we'll solve one equation for one variable and substitute it into the other equation.
Let's solve the first equation for y:
2x + y = 6
Subtract 2x from both sides:
y = 6 - 2x
Now, substitute this value of y into the second equation:
5x - 2(6 - 2x) = 6
Distribute -2 to 6 - 2x:
5x - 12 + 4x = 6
Combine like terms:
9x - 12 = 6
Add 12 to both sides:
9x = 6 + 12
9x = 18
Divide both sides by 9:
x = 18/9
x = 2
Now substitute this value back into the first equation to find y:
2(2) + y = 6
4 + y = 6
Subtract 4 from both sides:
y = 6 - 4
y = 2
Therefore, the solution to the system of equations is x = 2 and y = 2.
To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation.
Let's solve the first equation, 2x + y = 6, for y.
We can isolate y by subtracting 2x from both sides:
y = 6 - 2x
Now, substitute the expression for y in the second equation, 5x - 2y = 6, with the value we found:
5x - 2(6 - 2x) = 6
Distribute -2 to both terms inside the parentheses:
5x - 12 + 4x = 6
Combine like terms:
9x - 12 = 6
Add 12 to both sides:
9x = 18
Divide both sides by 9:
x = 2
Now that we have the value of x, we can substitute it back into the first equation to find y:
2(2) + y = 6
4 + y = 6
Subtract 4 from both sides:
y = 2
Thus, the solution to the system of equations is x = 2 and y = 2.