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3 years ago

Create a system of equations with a solution of (5,-2)

Mathematics

1 answer:

VladimirAG [237]3 years ago

5 0

<h3>5x - y = 27 and 2x + y = 8 are the system of equations with a solution of (5,-2) </h3>

<em><u>Solution:</u></em>

Given that,

create a system of equations with a solution of (5,-2)

<em><u>The equation for a line in slope intercept form:</u></em>

y = mx + b

Where, m is the slope and b is the y intercept

For (x, y) = (5, -2)

-2 = 5m + b

-2 = 5(5) + b

-2 = 25 + b

b = -2 - 25

b = -27

-2 = 5(-2) + b

-2 = -10 + b

b = 8

<em><u>Thus equations are:</u></em>

y = 5x - 27

y = -2x + 8

<em><u>Rearranging to standard form,</u></em>

5x - y = 27 --- eqn 1

2x + y = 8 ---- eqn 2

Thus the system of equations are found

<h3><u>Verify:</u></h3>

Solve eqn 1 and eqn 2

Add both eqn 1 and eqn 2

7x = 35

Substitute x = 5 in eqn 2

2(5) + y = 8

y = 8 - 10

Thus solution is (5, -2) and the found system of equations are correct

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Create a system of equations with a solution of (5,-2)​

Create a system of equations with a solution of (5,-2)