Solve 5t - 3 = 3t - 5 14 | 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

$$\left. \begin{array} { l } { 5 t - 3 = 3 t - 5 } \\ { 5 x - 1 = 14 - x } \end{array} \right.$$

Solve for t, x

$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$
$t=-1$

Solution Steps

Consider the first equation. Subtract $3t$ from both sides.

$$5t-3-3t=-5$$

Combine $5t$ and $-3t$ to get $2t$.

$$2t-3=-5$$

Add $3$ to both sides.

$$2t=-5+3$$

Add $-5$ and $3$ to get $-2$.

$$2t=-2$$

Divide both sides by $2$.

$$t=\frac{-2}{2}$$

Divide $-2$ by $2$ to get $-1$.

$$t=-1$$

Consider the second equation. Add $x$ to both sides.

$$5x-1+x=14$$

Combine $5x$ and $x$ to get $6x$.

$$6x-1=14$$

Add $1$ to both sides.

$$6x=14+1$$

Add $14$ and $1$ to get $15$.

$$6x=15$$

Divide both sides by $6$.

$$x=\frac{15}{6}$$

Reduce the fraction $\frac{15}{6}$ to lowest terms by extracting and canceling out $3$.

$$x=\frac{5}{2}$$

The system is now solved.

$$t=-1$$ $$x=\frac{5}{2}$$