Answer:
x=2 y=−1 so (2,-1)
Step-by-step explanation:
2x+y=3
x=3y+5
Consider the second equation. Subtract 3y from both sides.
x−3y=5
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the results for that variable in the other equation.
2x+y=3,x−3y=5
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
2x+y=3
Subtract y from both sides of the equation.
2x=−y+3
Divide both sides by 2.
x=1/2(−y+3)
Multiply 1/2 times −y+3.
x=−1/2y+3/2
Substitute y+3/2 for x in the other equation, x−3y=5.
−1/2y+3/2−3y=5
Add −y/2 to −3y.
−7/2y+3/2=5
Subtract 3/2 from both sides of the equation.
−7/2y=7/2
Divide both sides of the equation by −7/2, which is the same as multiplying both sides by the reciprocal of the fraction.
y=−1
Substitute −1 for y in x=−1/2y+3/2. Because the resulting equation contains only one variable, you can solve for x directly.
x=−1/2(−1)+3/2
Multiply −1/2 times −1.
x=1+3/2
Add 3/2 to 1/2 by finding a common denominator and adding numerators. Then reduce the fraction to the lowest terms if possible.
x=2
The system is now solved.
x=2,y=−1
Graph for reference:
