Solve the System of Equations 2/3x+5/2y=15 4x+15y=12

$\frac{2}{3} x + \frac{5}{2} y = 15$ $4 x + 15 y = 12$

Step 1

Solve for $x$ in $4 x + 15 y = 12$ .

Subtract $15 y$ from both sides of the equation.

$4 x = 12 - 15 y$

$\frac{2}{3} x + \frac{5}{2} y = 15$

Divide each term in $4 x = 12 - 15 y$ by $4$ and simplify.

Divide each term in $4 x = 12 - 15 y$ by $4$ .

$\frac{4 x}{4} = \frac{12}{4} + \frac{- 15 y}{4}$

$\frac{2}{3} x + \frac{5}{2} y = 15$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{12}{4} + \frac{- 15 y}{4}$

$\frac{2}{3} x + \frac{5}{2} y = 15$

Divide $x$ by $1$ .

$x = \frac{12}{4} + \frac{- 15 y}{4}$

$\frac{2}{3} x + \frac{5}{2} y = 15$

$x = \frac{12}{4} + \frac{- 15 y}{4}$

$\frac{2}{3} x + \frac{5}{2} y = 15$

$x = \frac{12}{4} + \frac{- 15 y}{4}$

$\frac{2}{3} x + \frac{5}{2} y = 15$

Simplify the right side.

Simplify each term.

Divide $12$ by $4$ .

$x = 3 + \frac{- 15 y}{4}$

$\frac{2}{3} x + \frac{5}{2} y = 15$

Move the negative in front of the fraction.

$x = 3 - \frac{15 y}{4}$

$\frac{2}{3} x + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

$\frac{2}{3} x + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

$\frac{2}{3} x + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

$\frac{2}{3} x + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

$\frac{2}{3} x + \frac{5}{2} y = 15$

Step 2

Replace all occurrences of $x$ with $3 - \frac{15 y}{4}$ in each equation.

Replace all occurrences of $x$ in $\frac{2}{3} x + \frac{5}{2} y = 15$ with $3 - \frac{15 y}{4}$ .

$\frac{2}{3} \cdot (3 - \frac{15 y}{4}) + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Simplify the left side.

Simplify $\frac{2}{3} \cdot (3 - \frac{15 y}{4}) + \frac{5}{2} y$ .

Simplify each term.

Apply the distributive property.

$\frac{2}{3} \cdot 3 + \frac{2}{3} \cdot (- \frac{15 y}{4}) + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2}{3} \cdot 3 + \frac{2}{3} \cdot (- \frac{15 y}{4}) + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Rewrite the expression.

$2 + \frac{2}{3} \cdot (- \frac{15 y}{4}) + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

$2 + \frac{2}{3} \cdot (- \frac{15 y}{4}) + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{15 y}{4}$ into the numerator.

$2 + \frac{2}{3} \cdot \frac{- 15 y}{4} + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Factor $2$ out of $4$ .

$2 + \frac{2}{3} \cdot \frac{- 15 y}{2 (2)} + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Cancel the common factor.

$2 + \frac{2}{3} \cdot \frac{- 15 y}{2 \cdot 2} + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Rewrite the expression.

$2 + \frac{1}{3} \cdot \frac{- 15 y}{2} + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

$2 + \frac{1}{3} \cdot \frac{- 15 y}{2} + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 15 y$ .

$2 + \frac{1}{3} \cdot \frac{3 (- 5 y)}{2} + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Cancel the common factor.

$2 + \frac{1}{3} \cdot \frac{3 (- 5 y)}{2} + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Rewrite the expression.

$2 + \frac{- 5 y}{2} + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

$2 + \frac{- 5 y}{2} + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Move the negative in front of the fraction.

$2 - \frac{5 y}{2} + \frac{5}{2} y = 15$

$x = 3 - \frac{15 y}{4}$

Combine $\frac{5}{2}$ and $y$ .

$2 - \frac{5 y}{2} + \frac{5 y}{2} = 15$

$x = 3 - \frac{15 y}{4}$

$2 - \frac{5 y}{2} + \frac{5 y}{2} = 15$

$x = 3 - \frac{15 y}{4}$

Combine the opposite terms in $2 - \frac{5 y}{2} + \frac{5 y}{2}$ .

Add $- \frac{5 y}{2}$ and $\frac{5 y}{2}$ .

$2 + 0 = 15$

$x = 3 - \frac{15 y}{4}$

Add $2$ and $0$ .

$2 = 15$

$x = 3 - \frac{15 y}{4}$

$2 = 15$

$x = 3 - \frac{15 y}{4}$

$2 = 15$

$x = 3 - \frac{15 y}{4}$

$2 = 15$

$x = 3 - \frac{15 y}{4}$

$2 = 15$

$x = 3 - \frac{15 y}{4}$

Step 3

Since $2 = 15$ is not true, there is no solution.

No solution

Step 4

Solve the System of Equations 2/3x+5/2y=15 4x+15y=12

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