Solve Delta*c + 2y = - 2; 3x - 6y = 6 | 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

$$\begin{cases}\Delta c+2y=-2\\ 3x-6y=6\end{cases}$$

Solve for x, y

$x=-c\Delta $
$y=-\frac{c\Delta }{2}-1$

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.

$$2y+c\Delta =-2,-6y+3x=6$$

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.

$$2y+c\Delta =-2$$

Subtract $\Delta c$ from both sides of the equation.

$$2y=-c\Delta -2$$

Divide both sides by $2$.

$$y=-\frac{c\Delta }{2}-1$$

Substitute $-1-\frac{\Delta c}{2}$ for $y$ in the other equation, $-6y+3x=6$.

$$-6\left(-\frac{c\Delta }{2}-1\right)+3x=6$$

Multiply $-6$ times $-1-\frac{\Delta c}{2}$.

$$3c\Delta +6+3x=6$$

Subtract $3\Delta c+6$ from both sides of the equation.

$$3x=-3c\Delta $$

Divide both sides by $3$.

$$x=-c\Delta $$

The system is now solved.

$$y=-\frac{c\Delta }{2}-1,x=-c\Delta $$