How do you solve #2(x-4) + y=6# and #3x-2(y-3)=13# using substitution?

Question

Avery Alexander · Accepted Answer

#(5,4)#

Substitution means rearranging one of the 2 equations in terms of x or y and substituting into the other equation.

Choosing #2(x-4)+y=6 # and rearranging to make y the subject.

distribute the bracket.

#2x-8+y=6#

subtract 2x from both sides.

#cancel(2x)cancel(-2x)-8+y=6-2x#

add 8 to both sides.

#cancel(-8)cancel(+8)+y=6+8-2x#

#rArry=14-2xlarrcolor(red)"y is now the subject"#

We can now substitute this into the other equation and solve for x.

#rArr3x-2(color(red)(14-2x)-3)=13#

#rArr3x-2(11-2x)=13#

#rArr3x-22+4x=13#

#rArr7x=35rArrx=35/7=5#

We have #y=14-2x" from above"# and substituting x = 5 will give corresponding value of y.

#x=5rArry=14-(2xx5)=14-10=4#

#"Thus solution is " x=5,y=4#

#color(blue)"As a check"#

#2(5-4)+4=2+4=6color(white)(xx)✔︎#

#"and " (3xx5)-2(4-3)=15-2=13color(white)(xx)✔︎#

Isaiah Anthony · Answer

undefined 1. Solve the first equation for $ y $:
   $$ 2(x-4) + y = 6 $$
   $$ y = 6 - 2(x-4) $$

2. Substitute the expression for $ y $ into the second equation:
   $$ 3x - 2(6 - 2(x-4) - 3) = 13 $$

3. Simplify and solve for $ x $.

4. Once you find the value of $ x $, substitute it back into one of the original equations to find the corresponding value of $ y $.