What is 4x+y=7,2x-y=12 ?

The solution to 4x+y=7,2x-y=12 is x= 19/6 ,y=-17/3

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4x+y=7,2x-y=12

4 x + y = 7, 2 x - y = 12

x = \frac{19}{6}, y = - \frac{17}{3}

Solution steps

[4 x + y = 7 2 x - y = 12]

Isolate

x

for

4 x + y = 7 : x = \frac{7 - y}{4}

Substitute

x = \frac{7 - y}{4}

[2 \cdot \frac{7 - y}{4} - y = 12]

Simplify

[\frac{7 - 3 y}{2} = 12]

Isolate

y

for

\frac{7 - 3 y}{2} = 12 : y = - \frac{17}{3}

For

x = \frac{7 - y}{4}

Substitute

y = - \frac{17}{3}

x = \frac{7 - ( - \frac{17}{3} )}{4}

\frac{7 - ( - \frac{17}{3} )}{4} = \frac{19}{6}

x = \frac{19}{6}

The solutions to the system of equations are:

x = \frac{19}{6}, y = - \frac{17}{3}

2 x + y = 19, 2 x - 3 y = - 3

3 x - 5 y - 6 = 2, x + 3 y - 6 = 0

2 x + 3 y = 32, 11 y - 9 x = 3

x - 4 y = - 5, 3 x - 8 y = 1

y = 2 x + 7, - 6 x - 2 y = - 4