How do you solve this system of equations: -5x + y = - 4 and 2x - y = - 5?

2 Answers
Dec 7, 2017

See a solution process below:

Explanation:

Step 1) Solve the first equation for y:

-5x + y = -4

color(red)(5x) - 5x + y = color(red)(5x) - 4

0 + y = 5x - 4

y = 5x - 4

Step 2) Substitute (5x - 4) for y in the second equation and solve for x:

2x - y = -5 becomes:

2x - (5x - 4) = -5

2x - 5x + 4 = -5

(2 - 5)x + 4 = -5

-3x + 4 = -5

-3x + 4 - color(red)(4) = -5 - color(red)(4)

-3x + 0 = -9

-3x = -9

(-3x)/color(red)(-3) = (-9)/color(red)(-3)

(color(ed)(cancel(color(black)(-3)))x)/cancel(color(red)(-3)) = 3

x = 3

Step 3) Substitute 3 for x in the solution to the first equation at the end of Step 1 and calculate y:

y = 5x - 4 becomes:

y = (5 xx 3) - 4

y = 15 - 4

y = 11

The Solution Is: x = 3 and y = 11 or (3, 11)

Dec 7, 2017

y=11, x=3

Explanation:

-5x+y=-4-------(1)

2x-y=-5--------(2)

:.(1)+(2)

:.-3x=-9

:.x=9/3

:.x=3

substitute x=3 in (2)

:.2(3)-y=-5

6-y=-5

:.-y=-5-6

:.-y=-11

:.y=11

~~~~~~~~~~~~~~

check:-

substitute y=11 and x=3 in (1)

:.-5(3)+(11)=-4

:.-15+11=-4

:.-4=-4