Identify the solution of the system of equations, if any.
-4x-2y+=4
8y+16x-16
Please proofread your post.
The second line is not an equation.
And what does 2y+= mean?
To find the solution of the system of equations, you can use the method of substitution or elimination. Let's use the method of elimination in this case.
Start by multiplying both sides of the first equation by 8 to make the coefficients of the x terms opposite:
-4x - 2y = 4 multiplied by 8 gives:
(-4x)(8) - (2y)(8) = (4)(8)
-32x - 16y = 32
Next, add the two equations:
-32x - 16y + 8y + 16x = 32 + -16
(-32x + 16x) + (-16y + 8y) = 16
-16y - 16x = 16
Now, divide both sides of the equation by -16 to solve for y:
(-16y - 16x)/-16 = 16/-16
y + x = -1
Now, let's substitute this expression for y into one of the original equations, say the second equation:
8y + 16x - 16 = 0
Substitute y + x = -1 for y:
8(y + x) + 16x - 16 = 0
8y + 8x + 16x - 16 = 0
8x + 16x - 16 + 16 = 0
24x = 0
Divide both sides by 24:
x = 0
Now, substitute x = 0 into y + x = -1:
y + 0 = -1
y = -1
Therefore, the solution to the system of equations is x = 0 and y = -1.