Question

Solve each system by substitution: -3x + 5y = -4
x - 5y = 18

Answer 1

`x=-7,\,y=-5`

Explanation:

Elimination

`-3x+5y=-4\\x-5y=18\\\\-3x+x=-4+18\\-2x=14\\x=-7\\\\x-5y=18\\(-7)-5y=18\\-5y=25\\y=-5`

In the first step, you add the two equations to eliminate "y", and then it's easy to find x. Then, you substitute "x" back into either original equation and get "y" that way.

Substitution

`-3x+5y=-4\\x-5y=18\\\\x=5y+18\\\\-3x+5y=-4\\-3(5y+18)+5y=-4\\-15y-54+5y=-4\\-15y+5y=50\\-10y=50\\y=-5\\\\x=5(-5)+18=-25+18=-7`

In the first step, you solve the second equation for "x" and then plug that into the first equation, and then it's easy to find "y", and then "x".

Answer 2

To solve the system by substitution, we can solve one of the equations for one of the variables, and then substitute that expression into the other equation.

From the second equation, we can solve for x:

x - 5y = 18

x = 5y + 18

Now we can substitute this expression for x into the first equation:

-3x + 5y = -4

-3(5y + 18) + 5y = -4

-15y - 54 + 5y = -4

-10y = 50

y = -5

Now that we know y = -5, we can substitute this value back into the expression we found for x:

x = 5y + 18

x = 5(-5) + 18

x = -7

Therefore, the solution to the system of equations is x = -7 and y = -5.