Question

What is the solution to the following system: y=6x+5 and 5x-4y=-1

Answer 1

Answer:

(-1,-1)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer 2

Answer:

x= -1 and y= -1

Step-by-step explanation:

Power through with me as I explain this, its a bit long of an explanation.

To solve the following system of equations, we need to write 5x-4y=-1 in slope-intercept form.

$5x -4y= -1$

Subtract 5x from both sides.

$5x-5x -4y= -1 -5x$

$-4y= -1-5x$

Divide each term by -4.

$\frac{-4y}{-4} = \frac{-1}{-4} + \frac{-5x}{-4}$

Remember that dividing two negative values results in a positive value.

$y= \frac{1}{4} + \frac{5x}{4}$

Reorder the terms. (Reordering terms makes the work tidier, it does not change the result)

$y= \frac{5}{4} x+ \frac{1}{4}$

Now that we have the slope-intercept form, we can solve by subsitution with the two equations to find the solution.

Substitute $\frac{5}{4} x + \frac{1}{4}$ for y in $y= 6x+5$.

$\frac{5}{4} x+\frac{1}{4} = 6x + 5$

Subtract 1/4 from each side.

$\frac{5}{4}x+\frac{1}{4}-\frac{1}{4}=6x+5-\frac{1}{4}$

Simplify the left side.

$\frac{5}{4}x=6x+5 -\frac{1}{4}$

Simplify the right side.

$\frac{5}{4}x=6x+\frac{19}{4}$

Subtract 6x from both sides.

$\frac{5}{4}x-6x=6x+\frac{19}{4}-6x$

Simplify.

$\frac{5}{4}x-6x=\frac{19}{4}$

Simplify the left side of the equation by factoring out x.

$x(\frac{5}{4} -6)= \frac{19}{4}$

$x(-\frac{19}{4} )=\frac{19}{4}$

$-\frac{19}{4} x=\frac{19}{4}$

Multiply each side by 4.

$4\left(-\frac{19}{4}x\right)=\frac{19*4}{4}$

$-19x=19$

Divide both side by 19.

$\frac{-19x}{-19}=\frac{19}{-19}$

$x= -1$

Now that we know the value of x, we need to find y.

Insert the value of x in the equation y= 6x+5

$y= 6(-1) +5$

$y=-6+5$

$y=-1$

Thus, x= -1 and y= -1 OR (-1,-1)