Question

7. Solve the system of linear equations. - 3x + 5y = 4 x + y = -4 A. (1, -5) B. (0, -4) C. (-3,-1) D. (-5, 1)

Answer 1

To solve this system of equations, we can use the substitution method. In this way, we can solve the system for one of the unknowns. Then, we need to substitute the resulting value in one of the equations to find the other value for the other unknown. We can proceed as follows:

`x+y=-4\Rightarrow x=-4-y`

We can substitute this in the other equation as follows:

`-3(-4-y)+5y=4`

Now, we need to apply the distributive property:

`12+3y+5y=4\Rightarrow12+8y=4`

Subtracting by 12 to both sides of the equation:

`12-12+8y=4-12\Rightarrow8y=-8`

Dividing both sides by 8, we have:

`(8y)/(8)=-(8)/(8)\Rightarrow y=-1`

Now, with a value of y = -1, we can substitute this one into the easiest equation to find the value of x:

`x+(-1)=-4\Rightarrow x=-4+1\Rightarrow x=-3`

Therefore, we have that the solution for this system is:

• x = -3

,

• y = -1, or

,

• (-3, -1) (option C).