Question

-Solve this system of equations using the substitution method.y = 5x - 3y = -6x + 8Because both equations equal y, we can substitute one of theequations forh). This will create an equation with only one variable, X.5x – 3 = -6x + 8[?]x – 3 = 8Hint: First add 6x to each side of the equation.

Answer 1

The solution to the system of equations is x = 1 and y = 2.

To solve the system of equations using the substitution method, we start with the given system:

Equation 1: y = 5x - 3

Equation 2: y = -6x + 8

Since both equations are set equal to y, we can set them equal to each other:

5x - 3 = -6x + 8

To solve for x, we can isolate the x term by adding 6x to both sides:

11x - 3 = 8

Next, add 3 to both sides to further isolate the x term:

11x = 11

Now, divide both sides by 11 to solve for x:

x = 1

Now that we have the value for x, substitute it back into one of the original equations to find y. Let's use the first equation:

y = 5(1) - 3

This simplifies to y = 2.

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

Answer 2

Given the system of equations:

`\begin{cases}y={5x-3} \\ y={-6x+8}\end{cases}`

We solve it using the substitution method, then:

`5x-3=-6x+8`

We add 6x on both sides of the equation:

`\begin{gathered} 5x-3+6x=-6x+8+6x \\ 11x-3=8 \end{gathered}`

Now, we add 3 on both sides:

`\begin{gathered} 11x-3+3=8+3 \\ 11x=11 \end{gathered}`

Finally, we divide by 11 on both sides:

`\begin{gathered} (11x)/(11)=(11)/(11) \\ \\ \therefore x=1 \end{gathered}`

And the solution is:

`\begin{gathered} x=1 \\ y=2 \end{gathered}`