Solve -9x-6y=15,9x10y=145 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$-9x-6y=15,9x10y=145$$

Solve for x, y

$x=-\frac{5}{3}-\frac{290}{27x_{10}}$
$y=\frac{145}{9x_{10}}$
$x_{10}\neq 0$

Steps Using Substitution

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$9x_{10}y=145,-6y-9x=15$$

Pick one of the two equations which is more simple to solve for $y$ by isolating $y$ on the left hand side of the equal sign.

$$9x_{10}y=145$$

Divide both sides by $9x_{10}$.

$$y=\frac{145}{9x_{10}}$$

Substitute $\frac{145}{9x_{10}}$ for $y$ in the other equation, $-6y-9x=15$.

$$-6\times \frac{145}{9x_{10}}-9x=15$$

Multiply $-6$ times $\frac{145}{9x_{10}}$.

$$-\frac{290}{3x_{10}}-9x=15$$

Add $\frac{290}{3x_{10}}$ to both sides of the equation.

$$-9x=15+\frac{290}{3x_{10}}$$

Divide both sides by $-9$.

$$x=-\frac{5}{3}-\frac{290}{27x_{10}}$$

The system is now solved.

$$y=\frac{145}{9x_{10}},x=-\frac{5}{3}-\frac{290}{27x_{10}}$$