Algebra Examples

$y = 6 x - 7$ $- 5 x + y = - 6$

Step 1

Replace all occurrences of $y$ with $6 x - 7$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $- 5 x + y = - 6$ with $6 x - 7$ .

$- 5 x + 6 x - 7 = - 6$

$y = 6 x - 7$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $- 5 x + 6 x - 7$ .

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Step 1.2.1.1

Remove parentheses.

$- 5 x + 6 x - 7 = - 6$

$y = 6 x - 7$

Step 1.2.1.2

Add $- 5 x$ and $6 x$ .

$x - 7 = - 6$

$y = 6 x - 7$

$x - 7 = - 6$

$y = 6 x - 7$

$x - 7 = - 6$

$y = 6 x - 7$

$x - 7 = - 6$

$y = 6 x - 7$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $7$ to both sides of the equation.

$x = - 6 + 7$

$y = 6 x - 7$

Step 2.2

Add $- 6$ and $7$ .

$x = 1$

$y = 6 x - 7$

$x = 1$

$y = 6 x - 7$

Step 3

Replace all occurrences of $x$ with $1$ in each equation.

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Step 3.1

Replace all occurrences of $x$ in $y = 6 x - 7$ with $1$ .

$y = 6 (1) - 7$

$x = 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $6 (1) - 7$ .

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Step 3.2.1.1

Multiply $6$ by $1$ .

$y = 6 - 7$

$x = 1$

Step 3.2.1.2

Subtract $7$ from $6$ .

$y = - 1$

$x = 1$

$y = - 1$

$x = 1$

$y = - 1$

$x = 1$

$y = - 1$

$x = 1$

Step 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(1, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, - 1)$

Equation Form:

$x = 1, y = - 1$

Step 6