Question

Solve system of equations y=x-7, y=8x-70

Answer 1

To solve the system of equations y = x - 7 and y = 8x - 70, you can use the substitution method or the elimination method. The solutions to the system are x = 9 and y = 2, or x = 5 and y = -2.

Step-by-step explanation:

To solve the system of equations y = x - 7 and y = 8x - 70, we can use the substitution method or the elimination method.

Substitution Method:

1. Using the first equation, substitute x - 7 for y in the second equation: x - 7 = 8x - 70.
2. Simplify the equation: 7x = 63.
3. Divide both sides of the equation by 7: x = 9.
4. Substitute this value of x back into the first equation: y = 9 - 7 = 2.

Therefore, the solution to the system of equations is x = 9 and y = 2.

Elimination Method:

1. Multiply the first equation by 8 to make the coefficients of y the same in both equations: 8y = 8x - 56.
2. Subtract the second equation from the modified first equation to eliminate the y terms: 8y - y = 8x - 56 - (8x - 70).
3. Simplify the equation: 7y = -14.
4. Divide both sides of the equation by 7: y = -2.
5. Substitute this value of y back into either of the original equations to find x: x = -2 + 7 = 5.

Therefore, the solution to the system of equations is x = 5 and y = -2.