solve the following simultaneous linear equation graphically 3x+4y=2 y=x+6
Answers
Answer:
3x+4y=2y=x+6
Consider the first equation. Subtract 2y from both sides.
3x+4y−2y=0
Combine 4y and −2y to get 2y.
3x+2y=0
Consider the second equation. Subtract x from both sides.
2y−x=6
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.
3x+2y=0,−x+2y=6
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
3x+2y=0
Subtract 2y from both sides of the equation.
3x=−2y
Divide both sides by 3.
x=
3
1
(−2)y
Multiply
3
1
times −2y.
x=−
3
2
y
Substitute −
3
2y
for x in the other equation, −x+2y=6.
−(−
3
2
)y+2y=6
Multiply −1 times −
3
2y
.
3
2
y+2y=6
Add
3
2y
to 2y.
3
8
y=6
Divide both sides of the equation by
3
8
, which is the same as multiplying both sides by the reciprocal of the fraction.
y=
4
9
Substitute
4
9
for y in x=−
3
2
y. Because the resulting equation contains only one variable, you can solve for x directly.
x=−
3
2
×(
4
9
)
Multiply −
3
2
times
4
9
by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.
x=−
2
3
The system is now solved.
x=−
2
3
,y=
4
9
Step-by-step explanation: