Which of these systems of equations have a solution of (-2,4) ? Select all that apply. y=x+6 y=-x-6 10x-y=16 5x+y=-6 x+3y=10 -2x-y=0 x-y=-6 4x+2y=16 x+y=2 y=2x+8 y=4 x=-2

To determine which systems of equations have a solution of $(-2,4)$, we need to substitute the coordinates $x=-2$ and $y=4$ into each equation and see if they hold true.<br /><br />Let's go through each equation one by one:<br /><br />1. $y=x+6$<br /> Substituting $x=-2$ and $y=4$:<br /> $4 = -2 + 6$<br /> $4 = 4$ (True)<br /><br />2. $y=-x-6$<br /> Substituting $x=-2$ and $y=4$:<br /> $4 = -(-2) - 6$<br /> $4 = 2 - 6$<br /> $4 = -4$ (False)<br /><br />3. $10x-y=16$<br /> Substituting $x=-2$ and $y=4$:<br /> $10(-2) - 4 = 16$<br /> $-20 - 4 = 16$<br /> $-24 = 16$ (False)<br /><br />4. $5x+y=-6$<br /> Substituting $x=-2$ and $y=4$:<br /> $5(-2) + 4 = -6$<br /> $-10 + 4 = -6$<br /> $-6 = -6$ (True)<br /><br />5. $x+3y=10$<br /> Substituting $x=-2$ and $y=4$:<br /> $-2 + 3(4) = 10$<br /> $-2 + 12 = 10$<br /> $10 = 10$ (True)<br /><br />6. $-2x-y=0$<br /> Substituting $x=-2$ and $y=4$:<br /> $-2(-2) - 4 = 0$<br /> $4 - 4 = 0$<br /> $0 = 0$ (True)<br /><br />7. $x-y=-6$<br /> Substituting $x=-2$ and $y=4$:<br /> $-2 - 4 = -6$<br /> $-6 = -6$ (True)<br /><br />8. $4x+2y=16$<br /> Substituting $x=-2$ and $y=4$:<br /> $4(-2) + 2(4) = 16$<br /> $-8 + 8 = 16$<br /> $0 = 16$ (False)<br /><br />9. $x+y=2$<br /> Substituting $x=-2$ and $y=4$:<br /> $-2 + 4 = 2$<br /> $2 = 2$ (True)<br /><br />10. $y=2x+8$<br /> Substituting $x=-2$ and $y=4$:<br /> $4 = 2(-2) + 8$<br /> $4 = -4 + 8$<br /> $4 = 4$ (True)<br /><br />11. $y=4$<br /> Substituting $x=-2$ and $y=4$:<br /> $4 = 4$ (True)<br /><br />12. $x=-2$<br /> Substituting $x=-2$ and $y=4$:<br /> $-2 = -2$ (True)<br /><br />Therefore, the systems of equations that have a solution of $(-2,4)$ are:<br />- $y=x+6$<br />- $5x+y=-6$<br />- $x+3y=10$<br />- $-2x-y=0$<br />- $x-y=-6$<br />- $x+y=2$<br />- $y=2x+8$<br />- $y=4$<br />- $x=-2$