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


Sagot :

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:

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.

[tex]5x -4y= -1[/tex]

Subtract 5x from both sides.

[tex]5x-5x -4y= -1 -5x[/tex]

[tex]-4y= -1-5x[/tex]

Divide each term by -4.

[tex]\frac{-4y}{-4} = \frac{-1}{-4} + \frac{-5x}{-4}[/tex]

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

[tex]y= \frac{1}{4} + \frac{5x}{4}[/tex]

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

[tex]y= \frac{5}{4} x+ \frac{1}{4}[/tex]

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

Substitute [tex]\frac{5}{4} x + \frac{1}{4}[/tex] for y in [tex]y= 6x+5[/tex].

[tex]\frac{5}{4} x+\frac{1}{4} = 6x + 5[/tex]

Subtract 1/4 from each side.

[tex]\frac{5}{4}x+\frac{1}{4}-\frac{1}{4}=6x+5-\frac{1}{4}[/tex]

Simplify the left side.

[tex]\frac{5}{4}x=6x+5 -\frac{1}{4}[/tex]

Simplify the right side.

[tex]\frac{5}{4}x=6x+\frac{19}{4}[/tex]

Subtract 6x from both sides.

[tex]\frac{5}{4}x-6x=6x+\frac{19}{4}-6x[/tex]

Simplify.

[tex]\frac{5}{4}x-6x=\frac{19}{4}[/tex]

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

[tex]x(\frac{5}{4} -6)= \frac{19}{4}[/tex]

[tex]x(-\frac{19}{4} )=\frac{19}{4}[/tex]

[tex]-\frac{19}{4} x=\frac{19}{4}[/tex]

Multiply each side by 4.

[tex]4\left(-\frac{19}{4}x\right)=\frac{19*4}{4}[/tex]

[tex]-19x=19[/tex]

Divide both side by 19.

[tex]\frac{-19x}{-19}=\frac{19}{-19}[/tex]

[tex]x= -1[/tex]

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

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

[tex]y= 6(-1) +5[/tex]

[tex]y=-6+5[/tex]

[tex]y=-1[/tex]

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