Question

7x + 11y = -2

7x + 3y = 30
Solve this without graphing

A) x = 4, y = 6
B) x = 6, y = -4
C) x = -4, y = 6
D) x = 6, y = 4

Answer 1

To solve the system of equations without graphing, we can use the method of substitution or elimination. Using the method of elimination, we can multiply one of the equations by a scalar to eliminate one of the variables. Then we can subtract the two equations to solve for the remaining variable. Finally, we can substitute the value of the remaining variable into one of the equations to solve for the other variable.

Step-by-step explanation:

To solve the system of equations without graphing, we can use the method of substitution or elimination.

Let's use the method of elimination:

1. Multiply the second equation by -4 to eliminate the x terms: -28x - 12y = -120.
2. Subtract the new equation from the first equation: (7x + 11y) - (-28x - 12y) = -2 - (-120).
3. Simplify the equation: 35x + 23y = 118.
4. Now, solve the system of equations: 35x + 23y = 118 and 7x + 11y = -2.
5. Multiply the second equation by 5 to make the coefficients of x the same: 35x + 55y = -10.
6. Subtract the new equation from the equation we simplified earlier: (35x + 23y) - (35x + 55y) = 118 - (-10).
7. Simplify the equation: -32y = 128.
8. Divide both sides of the equation by -32: y = 6.
9. Substitute the value of y into either of the original equations to solve for x: 7x + 11(6) = -2.
10. Simplify the equation: 7x + 66 = -2.
11. Subtract 66 from both sides of the equation: 7x = -68.
12. Divide both sides of the equation by 7: x = -8.

Therefore, the solution to the system of equations is x = -8 and y = 6.