GG.8 Solve a system of equations using substitution

Question

J8X
Solve using substitution.

2x − 6y = –8
x − 4y = –8

Answer 1

To solve the system of equations using substitution, we have the following equations:

1. $2x-6y=-8$ (Equation 1)
2. $x-4y=-8$ (Equation 2)

We can start with Equation 2 and solve for $x$:

$$x=4y-8$$

Now that we have $x$ in terms of $y$, we can substitute this expression into Equation 1:

$$2(4y-8)-6y=-8$$

Next, simplify and solve for $y$:

1. Distribute $2$ in the first term:

   $$8y-16-6y=-8$$

2. Combine like terms:

   $$2y-16=-8$$

3. Add $16$ to both sides:

   $$2y=8$$

4. Divide by $2$:

   $$y=4$$

Now that we have the value of $y$, we substitute it back into the expression we found for $x$:

$$x=4(4)-8$$

Calculate $x$:

$$x=16-8=8$$

Thus, the solution to the system of equations is:

$$(x,y)=(8,4)$$

To verify, plug the values back into the original equations:

1. For Equation 1: $$2(8)-6(4)=16-24=-8\text{(True)}$$

2. For Equation 2: $$8-4(4)=8-16=-8\text{(True)}$$

Both equations hold true, confirming that the solution is correct.

The solution is:

$$\boxed{{\displaystyle (8,4)}}$$