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 6x + y = 2
x − 4y = 2
The estimated solution is (, ).
The algebraic solution is

Answer 1

The estimated solution is (0,0 ).

The algebraic solution is ($\frac{2}{5},\frac{-2}{5})$

Step-by-step explanation:

We need to solve the system of equations:

$6x + y = 2\\x -4y = 2$

Solving using Elimination method

Let: $6x + y = 2\,\,eq(1)\\x -4y = 2\,\,eq(2)$

Multiply eq(1) by 4 and add eq(1) and eq(2)

$24x+4y=8\\x -4y = 2\\------\\25x=10\\x=\frac{10}{25}\\x=\frac{2}{5}$

So, value of x is $x=\frac{2}{5}$ Converting into whole number: x=0

Now finding value of y

Putting value of x into eq(1)

$6x+y=2\\6(\frac{2}{5})+y=2\\\frac{12}{5}+y=2\\y=2-\frac{12}{5}\\y=\frac{10-12}{5}\\y=\frac{-2}{5}$

So, value of y is $y=\frac{-2}{5}$ Converting into whole number: y=0

The estimated solution is (0,0 ).

The algebraic solution is ($\frac{2}{5},\frac{-2}{5})$

Keywords: System of equations

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