Question

Solve the following system of equations using the elimination method.
5x + y = 9

–10x + 7y = 18

Answer 1

y = 4
x = 1



The first step is to multiply such that one variable is the negation of that same variable in the opposite equation:

10x + 2y = 18

-10x + 7y =18


Next, combine the equations:

9y = 36

Divide:

y = 4

Then, to solve for x, just put the value of y into the original equation.

5x + 4 = 9


Subtract 4 from 9:

5x = 5


Divide:

x = 1


And then, to check your answers, insert your variables into the other equations:

-10(1) + 7(4) = 18


Multiply your variables:

-10 + 28 = 18

Add 10 to 18:

28 = 28

And there you go!

Answer 2

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5x + y = 9

- 10x + 7y = 18 [tex]\rightarrow[/tex] (ii)

Now, multiplying "5x + y = 9" by 2 we get,

10x + 2y = 18$\rightarrow$ (i)

Now, using Elimination method.

So, we gotta subtract Equation (i) from Equation (ii)

Equation (i) - (ii)

$(10x + 2y) - ( - 10x + 7y) = 18 - 18 \\ \\ \implies \: 10x + 2y + 10x - 7y = 0 \\ \\ \implies \: \cancel{10x} + 2y + \cancel{10x} - 7y = 0 \\ \\ \implies - 5y = 0 \\ \\ \implies \: y = 5$

So, the value of "y" is 5. Now we gonna put the value of "y" in Equation (i).

$10x + 2y = 18 \\ \\ \implies \: 10x + 2 \times 5 = 18 \\ \\ \implies10x + 10 = 18 \\ \\ \implies10x = 18 - 10 \\ \\ \implies10x = 8 \\ \\ \implies \: x = \frac{8}{10} \\ \\ \implies \: x = \cancel{ \frac{8}{10}} \\ \\ \implies \: x = \frac{4}{5} \\ \\ \implies \: x = 0.8$

So, at the we've found the values of "x" and "y".

x = 0.8 and y = 5

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