Mathematics: 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

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Solve the system. estimate the solution first.

alexjedington

15.01.2022

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

The algebraic solution is (x, y) = $(\frac{9}{4} , \frac{-15}{4})$

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

$x = \frac{18}{8} = \frac{9}{4}$

$x = \frac{9}{4}$

Substitute the value of "x" in eqn 1

$3(\frac{9}{4}) + y = 3\\\\\frac{27}{4} + y = 3\\\\y = 3 - \frac{27}{4}\\\\y = \frac{12-27}{4}\\\\y = \frac{-15}{4}$

The estimated solution is given as:

Enter whole numbers for the estimated solution

$x = \frac{9}{4} = 2.25\\\\x \approx 2$

$y = \frac{-15}{4} = -3.75\\\\y \approx -4$

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

$x = \frac{9}{4}$

$y = \frac{-15}{4}$

Thus the solution is (x, y) = $(\frac{9}{4} , \frac{-15}{4})$

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