Solve by Graphing 5x+2y=7 10x+4y=14

$5 x + 2 y = 7$ $10 x + 4 y = 14$

Step 1

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

$2 y = 7 - 5 x$

$10 x + 4 y = 14$

Step 2

Divide each term in $2 y = 7 - 5 x$ by $2$ and simplify.

Divide each term in $2 y = 7 - 5 x$ by $2$ .

$\frac{2 y}{2} = \frac{7}{2} + \frac{- 5 x}{2}$

$10 x + 4 y = 14$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{7}{2} + \frac{- 5 x}{2}$

$10 x + 4 y = 14$

Divide $y$ by $1$ .

$y = \frac{7}{2} + \frac{- 5 x}{2}$

$10 x + 4 y = 14$

$y = \frac{7}{2} + \frac{- 5 x}{2}$

$10 x + 4 y = 14$

$y = \frac{7}{2} + \frac{- 5 x}{2}$

$10 x + 4 y = 14$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{7}{2} - \frac{5 x}{2}$

$10 x + 4 y = 14$

$y = \frac{7}{2} - \frac{5 x}{2}$

$10 x + 4 y = 14$

$y = \frac{7}{2} - \frac{5 x}{2}$

$10 x + 4 y = 14$

Step 3

Subtract $10 x$ from both sides of the equation.

$4 y = 14 - 10 x$

$y = \frac{7}{2} - \frac{5 x}{2}$

Step 4

Divide each term in $4 y = 14 - 10 x$ by $4$ and simplify.

Divide each term in $4 y = 14 - 10 x$ by $4$ .

$\frac{4 y}{4} = \frac{14}{4} + \frac{- 10 x}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{14}{4} + \frac{- 10 x}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Divide $y$ by $1$ .

$y = \frac{14}{4} + \frac{- 10 x}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{14}{4} + \frac{- 10 x}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{14}{4} + \frac{- 10 x}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $14$ and $4$ .

Factor $2$ out of $14$ .

$y = \frac{2 (7)}{4} + \frac{- 10 x}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 7}{2 \cdot 2} + \frac{- 10 x}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Cancel the common factor.

$y = \frac{2 \cdot 7}{2 \cdot 2} + \frac{- 10 x}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Rewrite the expression.

$y = \frac{7}{2} + \frac{- 10 x}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{7}{2} + \frac{- 10 x}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{7}{2} + \frac{- 10 x}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Cancel the common factor of $- 10$ and $4$ .

Factor $2$ out of $- 10 x$ .

$y = \frac{7}{2} + \frac{2 (- 5 x)}{4}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{7}{2} + \frac{2 (- 5 x)}{2 (2)}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Cancel the common factor.

$y = \frac{7}{2} + \frac{2 (- 5 x)}{2 \cdot 2}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Rewrite the expression.

$y = \frac{7}{2} + \frac{- 5 x}{2}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{7}{2} + \frac{- 5 x}{2}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{7}{2} + \frac{- 5 x}{2}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Move the negative in front of the fraction.

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{7}{2} - \frac{5 x}{2}$

$y = \frac{7}{2} - \frac{5 x}{2}$

Step 5

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$y = - \frac{5 x}{2} + \frac{7}{2}$

Step 6

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