Solve the system of linear equations. Check
your answer. Write your answer as an ordered pair with no spaces.
y=-2x+6
-4x-6y=4
To solve the system of linear equations, we can use either substitution or elimination method.
Let's solve it using the substitution method:
From the first equation, we have y = -2x + 6.
Substituting this value of y into the second equation, we get:
-4x - 6(-2x + 6) = 4.
Simplifying the equation:
-4x + 12x - 36 = 4,
8x - 36 = 4,
8x = 40,
x = 5.
Substituting this value of x back into the first equation, we get:
y = -2(5) + 6,
y = -10 + 6,
y = -4.
Therefore, the solution to the system of linear equations is (5, -4).
Now, let's check our answer by substituting the values of x and y into both equations:
For the first equation:
-4(5) - 6(-4) = 4,
-20 + 24 = 4,
4 = 4. (True)
For the second equation:
-4(5) - 6(-4) = 4,
-20 + 24 = 4,
4 = 4. (True)
Both equations are true when x = 5 and y = -4, so our answer is correct.