x+2y=1300,x+3y=1300 how to solve this question by substitution
Answers
Answer:
x = 200 , y = 300
Step-by-step explanation:
2x+3y=1300
x+2y=800
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
2x+3y=1300,x+2y=800
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
2x+3y=1300
Subtract 3y from both sides of the equation.
2x=−3y+1300
Divide both sides by 2.
x=
2
1
(−3y+1300)
Multiply
2
1
times −3y+1300.
x=−
2
3
y+650
Substitute −
2
3y
+650 for x in the other equation, x+2y=800.
−
2
3
y+650+2y=800
Add −
2
3y
to 2y.
2
1
y+650=800
Subtract 650 from both sides of the equation.
2
1
y=150
Multiply both sides by 2.
y=300
Substitute 300 for y in x=−
2
3
y+650. Because the resulting equation contains only one variable, you can solve for x directly.
x=−
2
3
×300+650
Multiply −
2
3
times 300.
x=−450+650
Add 650 to −450.
x=200
The system is now solved.
x=200,y=300