Solving steps:-
5x+3y=−4
y−2x=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.
5x+3y=−4,−2x+y=6
-->Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
5x+3y=−4
-->Subtract 3y from both sides of the equation.
5x=−3y−4
--> Divide both sides by 5.
x = 1/5(-3y - 4)
--> Multiply 1/5 −3y−4.
x = -3/5y - 4/5
--> Substitute -3y - 4/ 5 for x n the other equation, −2x+y=6.
-2 (-3/5y - 4/5) + y = 6
--> Multiply −2 times -3y - 4/ 5
6/5y + 8/5 + y = 6
--> Add 6y/5 to y
11/5y + 8/5 = 6
--> Subtract 8/5 from both sides of the equation.
11/5y = 22/5
--> Divide both sides of the equation by 11/5, which is the same as multiplying both sides by the reciprocal of the fraction.
y = 2
--> Substitute 2 for y in x= -3/5y - 4/5. Because the resulting equation contains only one variable, you can solve for x directly.
x = -3/5 x 2 - 4/5
--> Multiply -3/5 times 2.
x = -6 - 4/ 5
--> Add -4/5 to -6/5 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
x = -2
--> The equation is now solved.
Answer : x = -2, y = 2
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