Solve 5n + 7y = 3; 6x - 8y = 20 | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$5n+7y=3; 6x-8y=20$$

Solve for x, y

$x=\frac{82-20n}{21}$
$y=\frac{3-5n}{7}$

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.

$$7y+5n=3,-8y+6x=20$$

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.

$$7y+5n=3$$

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

$$7y=3-5n$$

Divide both sides by $7$.

$$y=\frac{3-5n}{7}$$

Substitute $\frac{3-5n}{7}$ for $y$ in the other equation, $-8y+6x=20$.

$$-8\times \frac{3-5n}{7}+6x=20$$

Multiply $-8$ times $\frac{3-5n}{7}$.

$$\frac{40n-24}{7}+6x=20$$

Subtract $\frac{-24+40n}{7}$ from both sides of the equation.

$$6x=\frac{164-40n}{7}$$

Divide both sides by $6$.

$$x=\frac{82-20n}{21}$$

The system is now solved.

$$y=\frac{3-5n}{7},x=\frac{82-20n}{21}$$