solve algebraically and check
y=8x+3
y=-4x-21
8x+3=-4x-21
+4x +4x
12x+3=-21
-3 -3
12x=-24
x=-2
y=8x+3
y=8(-2)+3
y=-16+3
y=-13
(-2,-13)
check
y=8x+3
-13=8(-2)+3
-13=-16+3
-13=-13
y=-4x-21
-13=-4(-2)-21
-13=8-21 so -13=-13
these check, so did I do this correctly?
Thanks for checking my work
Correct
thank you
Yes, you have correctly solved the system of equations algebraically and double-checked by substituting the values back into the original equations. Your solution of (x, y) = (-2, -13) satisfies both equations, which confirms its accuracy.
To solve the system algebraically, you started by setting the two equations equal to each other to eliminate the y-variable:
8x + 3 = -4x - 21
Next, you simplified the equation by combining like terms:
12x + 3 = -21
Then, you isolated the variable by subtracting 3 from both sides:
12x = -24
Finally, you solved for x by dividing both sides by 12:
x = -2
Once you found the value of x, you plugged it back into either of the original equations to find the corresponding value of y:
y = 8(-2) + 3
y = -16 + 3
y = -13
Therefore, the solution to the system of equations is (x, y) = (-2, -13). And as you checked, these values satisfy both equations, so your solution is correct. Well done!