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2 years ago

Linear equations in two variables

Mathematics

1 answer:

love history [14]2 years ago

5 0

Answer:

y=-4 is a function

Step-by-step explanation:

It passes the vertical line test, and each x has only one y, so it is a function.

x = -4 is NOT a function because one x has multiple y values. It does not pass the vertical line test.

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2 years ago

13x=-21-6y and -8x=36+6y

IgorLugansk [536]

Answer:

$x=3\\y=-10$

Step-by-step explanation:

$13x=-21-6y\\-8x=36+6y$

Let's take one of the equations and solve for x. I'll take the first one.

$13x=-21-6y$

Divide by 13.

$x=\frac{-21-6y}{13}$

Now replace x in the second equation.

$-8x=36+6y\\-8(\frac{-21-6y}{13} )=36+6y$

Distribute -8

$\frac{168+48y}{13}=36+6y$

Break down the fraction.

$\frac{168}{13}+\frac{48}{13}y=36+6y$

Subtract $\frac{168}{13}$

$\frac{48}{13}y=36+6y-\frac{168}{13}$

Subtract 6y

$\frac{48}{13}y-6y=36-\frac{168}{13}$

Combine like terms;

$\frac{48-13*6}{13}y=\frac{36*13-168}{13}$

Solve;

$\frac{48-78}{13}y=\frac{468-168}{13}$

Keep solving;

$\frac{-30}{13}y=\frac{300}{13}$

Multiply by the negative reciprocal of the fraction next to y.

$(-\frac{13}{30} )\frac{-30}{13}y=\frac{300}{13}(-\frac{13}{30} )$

On the right side; 13 and 13 become 1. 300/30 = 30/3 = 10

$y=-10$

After having found y, replace it in any of the equations to find x.

$13x=-21-6y\\13x=-21-6(-10)\\13x=-21+60\\13x=39\\x=\frac{39}{13}\\ x=3$

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