Answer:
Explanation:
x+y=5; x-y=3Adding both equations, we get:
2x = 8
x = 4Substituting the value of x in any of the equations:
x+y=5
4+y=5
y=1So the solution to this system of equations is: x=4, y=1.3x+y=11; y=x+3Substituting y=x+3 in the first equation:
3x+x+3=11
4x=8
x=2Substituting x=2 in the second equation:
y=x+3
y=2+3
y=5So the solution to this system of equations is: x=2, y=5.x+3y=0; 2x-y=-7Multiplying the second equation by 3 to eliminate y:
6x-3y=-21Adding both equations, we get:
7x=-21
x=-3Substituting x=-3 in the first equation:
x+3y=0
-3+3y=0
y=1So the solution to this system of equations is: x=-3, y=1.y=-3x-2; 6x+2y=-4Substituting y=-3x-2 in the second equation:
6x+2(-3x-2)=-4
6x-6x-4=-4
-4=-4This means that the two equations are equivalent and represent the same line. Therefore, there are infinitely many solutions to this system of equations.-4x+5y=27; x-6y=-2Multiplying the second equation by 5 to eliminate y:
5x-30y=-10Adding both equations, we get:
x-4x+5y-30y=-2+27
-x-25y=25
25y=-x-25
y=-(1/25)x-1Substituting y=-(1/25)x-1 in the first equation:
-4x+5(-(1/25)x-1)=27
-4x-5/5x-5=27
-9x=32
x=-32/9Substituting x=-32/9 in the expression for y:
y=-(1/25)(-32/9)-1
y=83/225So the solution to this system of equations is: x=-32/9, y=83/225.