Question

Solve the system. Estimate the solution first. Enter whole numbers for the estimated solution and improper fractions in simplest form for the algebraic solution.

braceleftze 3x + y = 3
5x − y = 15


The estimated solution is (, ).


The algebraic solution is

Answer 1

The estimated solution is (x, y) = (2, -4)

The algebraic solution is (x, y) =
`((9)/(4) , (-15)/(4))`

Solution:

Given system of equations are:

3x + y = 3 ---- eqn 1

5x - y = 15 ------- eqn 2

Let us solve the above system of equations

Add eqn 1 and eqn 2

3x + y + 5x - y = 3 + 15

8x + 0 = 18

8x = 18

`x = (18)/(8) = (9)/(4)`

`x = (9)/(4)`

Substitute the value of "x" in eqn 1

`3((9)/(4)) + y = 3\\\\(27)/(4) + y = 3\\\\y = 3 - (27)/(4)\\\\y = (12-27)/(4)\\\\y = (-15)/(4)`

The estimated solution is given as:

Enter whole numbers for the estimated solution

`x = (9)/(4) = 2.25\\\\x \approx 2`

`y = (-15)/(4) = -3.75\\\\y \approx -4`

Thus estimated solution is (x, y) = (2, -4)

The algebraic solution is given as:

Enter improper fractions in simplest form for the algebraic solution

In an improper fraction, the numerator is always greater than or equal to the denominator

`x = (9)/(4)`

`y = (-15)/(4)`

Thus the solution is (x, y) =
`((9)/(4) , (-15)/(4))`