# How do you solve this system of equations: -3v + 2w = - 1;5v - w = 4?

Nov 4, 2017

See explanation

#### Explanation:

....you have 2 equations in 2 unknowns. The general technique is:
1. Pick one of the equations (your choice, and either one will work, but you learn to pick the easier one) and re-write it so that one of the variables is expressed as a function of the other.

1. Substitute that functional definition of the variable into the other equation. This reduces the number of variables, turning it into an equation in one unknown, which you can solve.

2. Once you have solved for the value of one of the unknowns, use it to deduce the other.

Like so:

rewrite the second equation, in the form w = f(v).
...start by adding w to both sides, giving:

$5 v = w + 4$

...then subtract 4 from both sides:

$5 v - 4 = w$

...now substitute this definition of w (5v-4) into the other equation:

#-3v + 2(5v-4) = -1

$- 3 v + 10 v - 8 = - 1$

$7 v - 8 = - 1$

$7 v = 7$

$v = 1$

...now use your value for v to deduce w:

$5 \left(1\right) - w = 4$

$w = 1$

So both v and w = 1 in this case.

DOUBLE CHECK YOUR WORK (when you can, it'll save you some points, and makes your instructor think you care!)

Do this by plugging your values into the original equations, & make sure they work out:

$- 3 \left(1\right) + 2 \left(1\right) = - 1$ CHECK

$5 \left(1\right) - 1 = 4$ CHECK

GOOD LUCK