Solve the system:
"Equation 1":Equation 1: 3x+4y=273x+4y=27
"Equation 2":Equation 2: -8x+y=33−8x+y=33
Both equations are linear equations in standard form. The solution to the system is the point that the two lines have in common. The xx and yy coordinates will be determined by substitution.
Solve Equation 1 for xx.
3x+4y=273x+4y=27
3x=27-4y3x=27−4y
Divide both sides by 33.
x=27/3-(4y)/3x=273−4y3
Simplify.
x=9-(4y)/3x=9−4y3
Substitute 9-4y/39−4y3 for xx in Equation 2. Solve for yy.
-8x+y=33−8x+y=33
-8(9-(4y)/3)+y=33−8(9−4y3)+y=33
-72+(32y)/3+y=33−72+32y3+y=33
Multiply yy by 3/333 to create an equivalent fraction with 33 in the denominator.
-72+(32y)/3+yxx3/3=33−72+32y3+y×33=33
-72+(32y)/3+(3y)/3=33−72+32y3+3y3=33
-72+(35y)/3=33−72+35y3=33
Add 7272 to both sides.
(35y)/3=33+7235y3=33+72
Simplify.
(35y)/3=10535y3=105
Multiply both sides by 33.
35y=105xx335y=105×3
35y=31535y=315
Divide both sides by 3535
y=315/35y=31535
y=9y=9
Substitute 99 for yy in Equation 1. Solve for xx.
3x+4(9)=273x+4(9)=27
3x+36=273x+36=27
3x=27-363x=27−36
3x=-93x=−9
x=(-9)/3x=−93
x=-3x=−3
The solution is the point of intersection for the two lines, which is (-3,9)(−3,9).
graph{(3x+4y-27)(y-8x-33)=0 [-14.24, 11.07, 1.37, 14.03]}
