Question

-3y = -2x - 7
Solve the system.
-4X = -6y - 10

Answer 1

To solve the system of equations -3y = -2x - 7 and -4x = -6y - 10 using the method of substitution, we can follow the steps: solve one equation for one variable, substitute the expression into the other equation, solve for the remaining variable, substitute the value back, and check the solution. The solution to the system is x = -2 and y = 1.

Step-by-step explanation:

The given system of equations is:

-3y = -2x - 7

-4x = -6y - 10

To solve this system, we can use the method of substitution:

1. Start by solving one of the equations for one variable in terms of the other.
2. Substitute this expression into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute this value back into one of the original equations to find the value of the other variable.
5. Check your solution by substituting the values back into both equations.

Let's solve the system step-by-step:

1. We can solve the first equation for y in terms of x: -3y = -2x - 7 becomes y = (2/3)x + (7/3).
2. Substitute this expression for y into the second equation: -4x = -6((2/3)x + (7/3)) - 10.
3. Simplify the equation: -4x = -4x - 14x/3 - 14 - 10. Combine like terms: -4x = -4x - (42x + 84)/3.
4. Multiply through by 3 to eliminate the fractions: -12x = -12x - 42x - 84.
5. Add 12x to both sides of the equation: 0 = -42x - 84.
6. Add 42x to both sides of the equation: 42x = -84.
7. Divide both sides of the equation by 42: x = -84/42 = -2.
8. Substitute this value of x back into the expression for y: y = (2/3)(-2) + (7/3) = -4/3 + 7/3 = 3/3 = 1.
9. Check the solution: Substitute the values of x and y into both original equations and ensure they are true.

Therefore, the solution to the system of equations is x = -2 and y = 1.

Answer 2

Let us at first multiply the equations with -1
3y=2x +7
4x=6y+10
Now let us bring the x and y terms to the Left Hand Side
3y-2x=7
4x-6y=10
We can divide the second equation by 2 as it is a common factor
2x-3y=10
Next we use the elimination method to remove the common terms from both equations
3y-2x=7
-3y+2x=10
0=10
This is not possible...
So, this means that this system of equations have no solution.