Question

Solve this system algebraically.

7x - 2y = 4
5y +3x =10

Answer 1

Answer:The correct answer to this problem is letter D {(40/41, 58/41})

Explanation:

Had this on a quiz got it right

Answer 2

x =
`$ (40)/(41) $`

y =
`$ (58)/(41) $`

Explanation:

A system of two equation with two variables is given.

We solve it by eliminating one variable first.

The equations are:

`$ 7x - 2y = 4 \hspace{20mm} \hdots (1) $` and

`$ 3x + 5y = 10 \hspace{20mm} \hdots (2) $`

We can eliminate either x or y.

We will eliminate y.

To do that multiply Equation (1) by 5 and Equation (2) by 2.

We get:
`$ 35x - 10y = 20 $` and

`$ 6x + 10y = 20 $`

Adding these two equations, we get:

`$ 35x + 6x = 40 $`

`$ \implies 41x = 40 $`

⇒ x = 40/41

We substitute the value of 'x' in Equation (1) (Can be substituted in Equation (2) as well). We get:

2y = 7x - 4

⇒ 2y =
`$7((40)/(41)) - 4 $`

`$ \implies y = (140 - 82)/(41) $`

`$ \implies y = (58)/(41) $`

Therefore, (x, y) = (40/41, 58/41).