Question

Solve this system of linear equations. Separate
the x. and y-values with a comma.
- 7x + 3y = 22
4x + 2y = 10

Answer 1

Answer:

$(-\frac{7}{13},\frac{79}{13})$

Step-by-step explanation:

Given:

Two equations are given.

$- 7x + 3y = 22$------(1)

$4x + 2y = 10$----------(2)

Solve equation 1 for y.

$- 7x + 3y = 22$

$3y = 22+7x$

$y=\frac{22+7x}{3}$-----------(3)

Now, we substitute y value in equation 2.

$4x + 2(\frac{22+7x}{3}) = 10$

$\frac{12x + 2(22+7x)}{3} = 10$

$12x + 2(22+7x)=10\times 3$

$12x + 44+14x=30$

$26x=30-44$

$26x=-14$

$x=-\frac{14}{26}$

$x=-\frac{7}{13}$

Now, we substitute x value in equation 1.

$- 7(-\frac{7}{13}) + 3y = 22$

$\frac{7\times 7}{13} + 3y = 22$

$\frac{49}{13} + 3y = 22$

$3y = 22-\frac{49}{13}$

$3y = \frac{13\times 22-49}{13}$

$3y = \frac{286-49}{13}$

$y = \frac{237}{13\times 3}$

$y = \frac{237}{39}$

$y = \frac{79}{13}$

Therefore, the value of x and y is $(x=-\frac{7}{13},y = \frac{79}{13})$