{2x+5y=-4 {3x-y=11 help please?

Linear systems with no solutions have the same slope for both linear equations but different y-intercepts. this means that the equations are parallel. for example y=1+2x and y=2+2x does not have a solution because they both have a slope of 2x.

Linear systems with infinite solutions are actually the same equation if you completely simplify them and put them in the same form. for example, y=2+3x is the same equations as 2y-6x=4 because if you add 6x to both sides of the equation, then divide both sides of the equation by 2, you get y=2+3x. that means that these two graphs are directly aligned and all the points are solutions.

the solution to the linear system in the question is -2 because if you use the linear combinations method (as shown below, that is the answer you get)

3(2x+5y=-4) multiply both equations to get one variable to get the same coefficient (6x)

2(3x-y=11)

6x+15y=-12 subtract one equation from another

6x-2y=22

_________

0x+17y=-34

y=-2 divide both sides by 17

2x+5(-2)=-4 plug in the value of y to solve for x

2x-10=-4 multiply

2x=6 add 10 to both sides

x=3 divide both sides by 2

4(3x-2y) -3(2x-5y) First do the multiplications so you get 12x -8y -6x+15y (because -3 times -5 is +15) Then combine the x terms and the y terms (12x - 6 x and -8y +15y) This gives you 6x +7y That is as far as we can go