How to solve 2x+5,5=3x-2-7?

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$2x+5,5=3x-2-7?$$

Solve for x, y

$y = \frac{43}{3} = 14\frac{1}{3} \approx 14.333333333$

Solution Steps

Consider the first equation. Subtract $7$ from $-2$ to get $-9$.

$$5=3x-9$$

Swap sides so that all variable terms are on the left hand side.

$$3x-9=5$$

Add $9$ to both sides.

$$3x=5+9$$

Add $5$ and $9$ to get $14$.

$$3x=14$$

Divide both sides by $3$.

$$x=\frac{14}{3}$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=2\times \frac{14}{3}+5$$

Multiply $2$ and $\frac{14}{3}$ to get $\frac{28}{3}$.

$$y=\frac{28}{3}+5$$

Add $\frac{28}{3}$ and $5$ to get $\frac{43}{3}$.

$$y=\frac{43}{3}$$

The system is now solved.

$$x=\frac{14}{3}$$ $$y=\frac{43}{3}$$

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