Question

3x-y=6
-4x+2y=-8 solve using substitution method

Answer 1

To solve the system of equations using the substitution method, solve one equation for one variable in terms of the other variable, substitute the expression into the other equation, solve for the remaining variable, substitute the value back into an equation to find the other variable, and check the solution. In this case, the solution is x = 2 and y = 0.

Step-by-step explanation:

To solve the system of equations using the substitution method:

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

In this case, let's solve the first equation for x in terms of y:

3x - y = 6

3x = y + 6

x = (y + 6) / 3

Now, substitute this expression for x into the second equation:

-4x + 2y = -8

-4((y + 6) / 3) + 2y = -8

Simplifying:

-(4/3)(y + 6) + 2y = -8

Solving for y:

-4(y + 6) + 6y = -24

-4y - 24 + 6y = -24

2y = 0

y = 0

Now substitute this value of y back into the first equation to find x:

3x - 0 = 6

3x = 6

x = 2

Therefore, the solution to the system of equations is x = 2 and y = 0.