Solve \left\{ \begin{array} { c } {3x+2y=6} \\ { 5x+4

Evaluate

{3 x + 2 y = 6 5 x + 4 y = 8

Solve the equation for x

More Steps

{x = \frac{6 - 2 y}{3} 5 x + 4 y = 8

Substitute the given value of x into the equation 5 x + 4 y = 8

5 \times \frac{6 - 2 y}{3} + 4 y = 8

Simplify

\frac{5 ( 6 - 2 y )}{3} + 4 y = 8

Multiply both sides of the equation by LCD

(\frac{5 ( 6 - 2 y )}{3} + 4 y) \times 3 = 8 \times 3

Simplify the equation

More Steps

30 + 2 y = 8 \times 3

Simplify the equation

30 + 2 y = 24

Move the constant to the right side

2 y = 24 - 30

Subtract the terms

2 y = - 6

Multiply both sides of the equation by \frac{1}{2}

2 y \times \frac{1}{2} = - 6 \times \frac{1}{2}

Reduce the numbers

2 y \times \frac{1}{2} = - 3

Cancel out the greatest common factor 2

y = - 3

Substitute the given value of y into the equation x = \frac{6 - 2 y}{3}

x = \frac{6 - 2 ( - 3 )}{3}

Simplify the expression

x = 4

Calculate

{x = 4 y = - 3

Check the solution

More Steps

{x = 4 y = - 3

Solution

(x, y) = (4, - 3)