Find the solution to the system of equations.

Question

$$\{\begin{array}{l}y=-5x+6\\ \\ y=3x-2\end{array}$$
$$x=$$
$$y=$$

Answer 1

To solve the system of equations

$$\{\begin{array}{l}y=-5x+6y=3x-2\end{array}$$

we can set the two equations for $y$ equal to each other:

$$-5x+6=3x-2$$

Now, we will solve for $x$. First, we can add $5x$ to both sides:

$$6=3x+5x-2$$

This simplifies to:

$$6=8x-2$$

Next, we can add $2$ to both sides:

$$6+2=8x$$ $$8=8x$$

Now, divide both sides by $8$:

$$x=1$$

Now that we have the value of $x$, we can substitute it back into either of the original equations to find $y$. We’ll use the first equation:

$$y=-5(1)+6$$ $$y=-5+6$$ $$y=1$$

Thus, the solution to the system of equations is:

$$x=1,y=1$$

In summary:

$$x=1$$ $$y=1$$