Linear Algebra Examples

$2.5 x + 0.5 y = - 4$ , $5 x + y = - 7$

Step 1

Subtract $5 x$ from both sides of the equation.

$y = - 7 - 5 x$

$2.5 x + 0.5 y = - 4$

Step 2

Replace all occurrences of $y$ with $- 7 - 5 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $2.5 x + 0.5 y = - 4$ with $- 7 - 5 x$ .

$2.5 x + 0.5 (- 7 - 5 x) = - 4$

$y = - 7 - 5 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2.5 x + 0.5 (- 7 - 5 x)$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$2.5 x + 0.5 \cdot - 7 + 0.5 (- 5 x) = - 4$

$y = - 7 - 5 x$

Step 2.2.1.1.2

Multiply $0.5$ by $- 7$ .

$2.5 x - 3.5 + 0.5 (- 5 x) = - 4$

$y = - 7 - 5 x$

Step 2.2.1.1.3

Multiply $- 5$ by $0.5$ .

$2.5 x - 3.5 - 2.5 x = - 4$

$y = - 7 - 5 x$

$2.5 x - 3.5 - 2.5 x = - 4$

$y = - 7 - 5 x$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $2.5 x$ from $2.5 x$ .

$0 x - 3.5 = - 4$

$y = - 7 - 5 x$

Step 2.2.1.2.2

Simplify the expression.

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Step 2.2.1.2.2.1

Multiply $0$ by $x$ .

$0 - 3.5 = - 4$

$y = - 7 - 5 x$

Step 2.2.1.2.2.2

Subtract $3.5$ from $0$ .

$- 3.5 = - 4$

$y = - 7 - 5 x$

$- 3.5 = - 4$

$y = - 7 - 5 x$

$- 3.5 = - 4$

$y = - 7 - 5 x$

$- 3.5 = - 4$

$y = - 7 - 5 x$

$- 3.5 = - 4$

$y = - 7 - 5 x$

$- 3.5 = - 4$

$y = - 7 - 5 x$

Step 3

Since $- 3.5 = - 4$ is not true, there is no solution.

No solution

Step 4