Solve by Substitution y=3x+19 and y=5x+33

$y = 3 x + 19$ and $y = 5 x + 33$

Step 1

Eliminate the equal sides of each equation and combine.

$3 x + 19 = 5 x + 33$

Step 2

Solve $3 x + 19 = 5 x + 33$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

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

$3 x + 19 - 5 x = 33$

Subtract $5 x$ from $3 x$ .

$- 2 x + 19 = 33$

Move all terms not containing $x$ to the right side of the equation.

Subtract $19$ from both sides of the equation.

$- 2 x = 33 - 19$

Subtract $19$ from $33$ .

$- 2 x = 14$

Divide each term in $- 2 x = 14$ by $- 2$ and simplify.

Divide each term in $- 2 x = 14$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{14}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{14}{- 2}$

Divide $x$ by $1$ .

$x = \frac{14}{- 2}$

Simplify the right side.

Divide $14$ by $- 2$ .

$x = - 7$

Step 3

Evaluate $y$ when $x = - 7$ .

Substitute $- 7$ for $x$ .

$y = 5 (- 7) + 33$

Simplify $5 (- 7) + 33$ .

Multiply $5$ by $- 7$ .

$y = - 35 + 33$

Add $- 35$ and $33$ .

$y = - 2$

Step 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 7, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 7, - 2)$

Equation Form:

$x = - 7, y = - 2$

Step 6

Solve by Substitution y=3x+19 and y=5x+33

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