Algebra Examples

$3 x + y = 2$ $4 x + y = 20$

Step 1

Subtract $3 x$ from both sides of the equation.

$y = 2 - 3 x$

$4 x + y = 20$

Step 2

Replace all occurrences of $y$ with $2 - 3 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $4 x + y = 20$ with $2 - 3 x$ .

$4 x + 2 - 3 x = 20$

$y = 2 - 3 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $4 x + 2 - 3 x$ .

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Step 2.2.1.1

Remove parentheses.

$4 x + 2 - 3 x = 20$

$y = 2 - 3 x$

Step 2.2.1.2

Subtract $3 x$ from $4 x$ .

$x + 2 = 20$

$y = 2 - 3 x$

$x + 2 = 20$

$y = 2 - 3 x$

$x + 2 = 20$

$y = 2 - 3 x$

$x + 2 = 20$

$y = 2 - 3 x$

Step 3

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

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Step 3.1

Subtract $2$ from both sides of the equation.

$x = 20 - 2$

$y = 2 - 3 x$

Step 3.2

Subtract $2$ from $20$ .

$x = 18$

$y = 2 - 3 x$

$x = 18$

$y = 2 - 3 x$

Step 4

Replace all occurrences of $x$ with $18$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = 2 - 3 x$ with $18$ .

$y = 2 - 3 \cdot 18$

$x = 18$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $2 - 3 \cdot 18$ .

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Step 4.2.1.1

Multiply $- 3$ by $18$ .

$y = 2 - 54$

$x = 18$

Step 4.2.1.2

Subtract $54$ from $2$ .

$y = - 52$

$x = 18$

$y = - 52$

$x = 18$

$y = - 52$

$x = 18$

$y = - 52$

$x = 18$

Step 5

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

$(18, - 52)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(18, - 52)$

Equation Form:

$x = 18, y = - 52$

Step 7