465x-75y=615 75x+465y=1005 solve by simultaneous eqaution
Answers
STEPS USING SUBSTITUTION
465x+75y=615
75x+465y=1005
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.
465x+75y=615,75x+465y=1005
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
465x+75y=615
Subtract 75y from both sides of the equation.
465x=−75y+615
Divide both sides by 465.
x=
465
1
(−75y+615)
Multiply
465
1
times −75y+615.
x=−
31
5
y+
31
41
Substitute
31
−5y+41
for x in the other equation, 75x+465y=1005.
75(−
31
5
y+
31
41
)+465y=1005
Multiply 75 times
31
−5y+41
.
−
31
375
y+
31
3075
+465y=1005
Add −
31
375y
to 465y.
31
14040
y+
31
3075
=1005
Subtract
31
3075
from both sides of the equation.
31
14040
y=
31
28080
Divide both sides of the equation by
31
14040
, which is the same as multiplying both sides by the reciprocal of the fraction.
y=2
Substitute 2 for y in x=−
31
5
y+
31
41
. Because the resulting equation contains only one variable, you can solve for x directly.
x=−
31
5
×2+
31
41
Multiply −
31
5
times 2.
x=
31
−10+41
Add
31
41
to −
31
10
by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
x=1
The system is now solved.
x=1,y=2
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