(2x+y=-8 y=2x+4)
Substitute y=2x+4 into the first equation:
2x+(2x+4)=-8
4x+4=-8
4x=-12
x=-3
Substitute x=-3 into the second equation:
y=2(-3)+4
y=-2
Therefore, the solution is (-3, -2).
(10x+3y=-11 8x+2y=-6)
Multiply both sides of the second equation by -1 to make the y-coefficient negative:
-8x - 2y = 6
Now we have two equations:
10x + 3y = -11
-8x - 2y = 6
We can eliminate y by adding the equations:
2x = -5
Solving for x gives x = -5/2.
Substituting x = -5/2 into either original equation gives:
10(-5/2) + 3y = -11
-25 + 3y = -11
3y = 14
y = 14/3
Therefore, the solution is (-5/2, 14/3).
To solve the system of equations (2x + y = -8, y = 2x + 4), we can use the method of substitution or the method of elimination. Let's use the method of substitution:
Step 1: Start with the second equation, y = 2x + 4.
Step 2: Substitute this value of y into the first equation, 2x + (2x + 4) = -8.
Step 3: Simplify the equation, 2x + 2x + 4 = -8.
Step 4: Combine like terms, 4x + 4 = -8.
Step 5: Move the constant term to the other side of the equation, 4x = -8 - 4.
Step 6: Simplify, 4x = -12.
Step 7: Divide both sides by 4 to solve for x, x = -12/4.
Step 8: Simplify, x = -3.
Step 9: Now substitute the value of x into either of the original equations to solve for y. Let's use the equation y = 2x + 4.
Step 10: Substitute x = -3 into y = 2x + 4, y = 2(-3) + 4.
Step 11: Simplify, y = -6 + 4.
Step 12: Combine like terms, y = -2.
The solution to the system of equations is x = -3 and y = -2.