-4x-y=-6
-8x-5y=-6
Solutions:
-4 -1 | -6
-8 -5 | -6
1) -4;-1;-6
2) -8;-5;-6
2x1-2
0;3;-6
x 1/3
0;1;-2 or y=-2
5x1-2
-12;0;-24
1;0;2 x=2
To find the solutions to the given system of equations, you can use the method of elimination or substitution. I will provide the steps for both methods so you can choose the one you prefer.
Method 1: Elimination
1. Multiply the first equation by 5 and the second equation by 1 to make the coefficients of y in both equations equal (-5 and -1, respectively).
-4x - y = -6 => -20x - 5y = -30
-8x - 5y = -6
2. Subtract the second equation from the first equation to eliminate the y variable.
(-20x - 5y) - (-8x - 5y) = -30 - (-6)
-20x - 5y + 8x + 5y = -30 + 6
-12x = -24
3. Simplify and solve for x.
-12x = -24
Divide by -12 (both sides): x = 2
4. Substitute the value of x back into one of the original equations (e.g., the first equation) to find y.
-4x - y = -6
-4(2) - y = -6
-8 - y = -6
Add 8 to both sides: -y = 2
Divide by -1 (both sides): y = -2
Therefore, the solution to the given system of equations is x = 2 and y = -2.
Method 2: Substitution
1. Solve one of the equations for one variable and substitute it into the other equation.
From the first equation, solve for y: y = -4x + 6.
Substitute this equation into the second equation:
-8x - 5(-4x + 6) = -6
2. Simplify and solve for x.
-8x + 20x - 30 = -6
12x - 30 = -6
Add 30 to both sides: 12x = 24
Divide by 12 (both sides): x = 2
3. Substitute the value of x back into one of the original equations (e.g., the first equation) to find y.
y = -4(2) + 6
y = -8 + 6
y = -2
Therefore, the solution to the given system of equations is x = 2 and y = -2.