How do you solve the following system using substitution?: #5x+2y=-4, -3x+y=20#

Question

Isaiah Anthony · Accepted Answer

#(x,y)to(-4,8)# #5x+2y=-4to(1)# #-3x+y=20to(2)# #"rearrange equation "(2)" to express y in terms of x"# #"add "3x" to both sides"# #rArry=20+3xto(3)# #color(blue)"substitute "y=20+3x" into equation "(1)# #5x+2(20+3x)=-4larr"distribute"# #rArr5x+40+6x=-4# #rArr11x+40=-4# #"subtract 40 from both sides"# #rArr11x=-44# #"divide both sides by 11"# #rArrx=(-44)/11=-4# #"substitute "x=-4" into equation "(3)# #rArry=20-12=8# #"the point of intersection "=(-4,8)#

Hazel Anglin · Answer

The solutions are #{x=-4 ; y=8}#

The equations are

#{(5x+2y=-4),(-3x+y=20):}#

#<=>#, #{(5x+2y=-4),(y=3x+20):}#

#<=>#, #{(5x+2(3x+20)=-4),(y=3x+20):}#

#<=>#, #{(11x+40=-4),(y=3x+20):}#

#<=>#, #{(11x=-44),(y=3x+20):}#

#<=>#, #{(x=-4),(y=3xx-4+20=8):}#

Eva Adamson · Answer

undefined To solve the system using substitution:
1. Solve one of the equations for one variable in terms of the other variable.
2. Substitute the expression found in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Once you have found the value of one variable, substitute it back into one of the original equations to find the value of the other variable.
5. Verify the solution by substituting the values of the variables into both original equations.

Let's solve the system:
Given equations:
1. $ 5x + 2y = -4 $
2. $ -3x + y = 20 $

From equation 2, solve for $ y $:
$ y = 20 + 3x $

Substitute $ 20 + 3x $ for $ y $ in equation 1:
$ 5x + 2(20 + 3x) = -4 $

Now, solve for $ x $:
$ 5x + 40 + 6x = -4 $
$ 11x + 40 = -4 $
$ 11x = -44 $
$ x = -4 $

Now that we have found the value of $ x $, substitute it back into equation 2 to find $ y $:
$ y = 20 + 3(-4) $
$ y = 20 - 12 $
$ y = 8 $

So, the solution to the system is $ x = -4 $ and $ y = 8 $.