How do you solve the system of equations $5 x + y = 11$ $5x + y = 11$ and $- 3 x - 7 y = - 13$ $- 3x - 7y = - 13$ ?

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Answer 1 · 2017-03-24T23:12:53

$x = 2$ $x = 2$

$y = 1$ $y = 1$

Solving by addition/ elimination
The plan is to eliminate either one of the variables; $y$ $y$ seems easier.

Eqn 1: $5 x + y = 11$ $" "5x + y = 11$

Eqn 2: $- 3 x - 7 y = - 13$ $" " -3x -7y = -13$

Multiply eqn 1 by $7$ $7$ to make it eqn 3:

$35 x + 7 y = 77$ $35x + 7y = 77$

Add eqn 3 + eqn 2:

$32 x = 64$ $32x = 64$

Dividing both sides by $32$ $32$ , we get

$x = 2$ $x = 2$

Substitute $x = 2$ $x = 2$ into any of the equations, let's say eqn 1 in this case

$5 \cdot (2) + y = 11$ $5 * (2) + y = 11$

$10 + y = 11$ $10 + y =11$

$y = 1$ $y = 1$

How do you solve the system of equations 5x+y=115x + y = 11 and −3x−7y=−13- 3x - 7y = - 13?