Question

Solve the following system using substitution.

Answer 1

Answer/Step-by-step explanation:

3. By substitution method, let's substitute $\frac{2}{3}x- 4$ for y in the first equation.

Thus,

$\frac{1}{3}x + 2(\frac{2}{3}x- 4) = 1$

Solve for x

$\frac{x}{3} + \frac{4x}{3} - 4 = 1$

Add 4 to both sides

$\frac{x}{3} + \frac{4x}{3} - 4 + 4 = 1 + 4$

$\frac{x}{3} + \frac{4x}{3} = 5$

$\frac{x + 4x}{3} = 5$

$\frac{5x}{3} = 5$

Multiply both sides by 3

$\frac{5x}{3}*3 = 5*3$

$5x = 15$

Divide both sides by 5

$x = 3$

Now, substitute 3 for x in the equation.

$y = \frac{2}{3}x- 4$

$y = \frac{2}{3}(3) - 4$

$y = 2 - 4$

$y = -2$

The solution of the equation is x = 3, y = -2

4. Solving by elimination, let's try to eliminate the x-variable by adding both equation together.

$3x - 2y = 11$

$-3x - y = 4$

            $-3y = 15$  => $(-3x +(-3x) = 0; -2y +(-y) = -3y; 11 + 4 = 15)$

Divide both sides by -3 to solve for y

$\frac{-3y}{-3} = \frac{15}{-3}$

$y = -5$

Substitute -5 for y in the first equation to find x

$3x - 2(-5) = 11$

$3x + 10 = 11$

Subtract 10 from both sides

$3x + 10 - 10 = 11 - 10$

$3x = 1$

Divide both sides by 3

$\frac{3x}{3} = \frac{1}{3}$

$x = \frac{1}{3}$

The solution is $x = \frac{1}{3}, y = -5$