Solve the system using substitution. Check your answer.
y=-2x+6
2y-x+3=0
The solution is
enter your response here.
(Simplify your answer. Type integers or simplified fractions. Type an ordered pair.)
To solve the system using substitution, we can substitute the expression for y from the first equation into the second equation.
From the first equation, we have y = -2x + 6.
Substituting this into the second equation:
2(-2x + 6) - x + 3 = 0
Simplifying the equation:
-4x + 12 - x + 3 = 0
-5x + 15 = 0
-5x = -15
x = -15 / -5
x = 3
Substituting this value of x back into the first equation:
y = -2(3) + 6
y = -6 + 6
y = 0
Therefore, the solution to the system is (3, 0).
Checking the answer:
Substituting these values into both equations:
y = -2(3) + 6
0 = -6 + 6
0 = 0
2(0) - 3 + 3 = 0
0 - 3 + 3 = 0
0 = 0
Both equations are true, so the solution is correct.