Solve the System of Equations 12y-21x=-5 y=7/4x+10

$12 y - 21 x = - 5$ $y = \frac{7}{4} x + 10$

Step 1

Combine $\frac{7}{4}$ and $x$ .

$y = \frac{7 x}{4} + 10$

$12 y - 21 x = - 5$

Step 2

Replace all occurrences of $y$ with $\frac{7 x}{4} + 10$ in each equation.

Replace all occurrences of $y$ in $12 y - 21 x = - 5$ with $\frac{7 x}{4} + 10$ .

$12 (\frac{7 x}{4} + 10) - 21 x = - 5$

$y = \frac{7 x}{4} + 10$

Simplify the left side.

Simplify $12 (\frac{7 x}{4} + 10) - 21 x$ .

Simplify each term.

Apply the distributive property.

$12 (\frac{7 x}{4}) + 12 \cdot 10 - 21 x = - 5$

$y = \frac{7 x}{4} + 10$

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$4 (3) (\frac{7 x}{4}) + 12 \cdot 10 - 21 x = - 5$

$y = \frac{7 x}{4} + 10$

Cancel the common factor.

$4 \cdot (3 (\frac{7 x}{4})) + 12 \cdot 10 - 21 x = - 5$

$y = \frac{7 x}{4} + 10$

Rewrite the expression.

$3 (7 x) + 12 \cdot 10 - 21 x = - 5$

$y = \frac{7 x}{4} + 10$

$3 (7 x) + 12 \cdot 10 - 21 x = - 5$

$y = \frac{7 x}{4} + 10$

Multiply $7$ by $3$ .

$21 x + 12 \cdot 10 - 21 x = - 5$

$y = \frac{7 x}{4} + 10$

Multiply $12$ by $10$ .

$21 x + 120 - 21 x = - 5$

$y = \frac{7 x}{4} + 10$

$21 x + 120 - 21 x = - 5$

$y = \frac{7 x}{4} + 10$

Combine the opposite terms in $21 x + 120 - 21 x$ .

Subtract $21 x$ from $21 x$ .

$0 + 120 = - 5$

$y = \frac{7 x}{4} + 10$

Add $0$ and $120$ .

$120 = - 5$

$y = \frac{7 x}{4} + 10$

$120 = - 5$

$y = \frac{7 x}{4} + 10$

$120 = - 5$

$y = \frac{7 x}{4} + 10$

$120 = - 5$

$y = \frac{7 x}{4} + 10$

$120 = - 5$

$y = \frac{7 x}{4} + 10$

Step 3

Since $120 = - 5$ is not true, there is no solution.

No solution

Step 4

Solve the System of Equations 12y-21x=-5 y=7/4x+10

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