Question

Find the solution to the system of equations.

You can use the interactive graph below to find the solution.
(y= -5x + 6
(y = 3x - 2
=
y =
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1-7 -6 -5 -4 -3 -2
1 2 3 4 5 6 7
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Answer 1

The solution for the given system of equations (x,y) is (1,1).

Explanation:

The given system of equations are
`y = -5x+6` and
`y = 3x-2`.

The given equations can be modified as :

`5x+y = 6` ----------(1)

`3x-y = 2` --------(2)

To solve the system of equations, you can use elimination method.

The first step is to add both the equations.

`5x+y = 6`

(+)
`3x-y = 2`

--------------------

8x = 8

⇒ x = 8/8

⇒ x = 1.

The x value is 1.

The second step is to substitute x = 1 in any of the two equations.

So, put x = 1 in equation (1),

⇒ 5(1) + y = 6

⇒ 5 + y = 6

Subtract 5 on both sides, to get y value.

⇒ 5+y-5 = 6-5

⇒ y = 1

The y value is 1.

The solution to the system of equations is be given by (x,y).

Therefore, the solution is (1,1).