Question

Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in the ordered-pair form given in Example 3. {4 x-3 y=28 {9 x-y=-6

Answer 1

To solve the given system of equations, you can use the method of substitution or elimination. By applying either method, we can find that the solution to the system is x = -2 and y = 6.

Step-by-step explanation:

To solve the given system of equations:

{ 4x - 3y = 28 }
{ 9x - y = -6 }

we can use the method of substitution or elimination.

Method 1: Substitution

1. From the second equation, we can isolate y to get y = 9x + 6.
2. Substitute this value of y into the first equation: 4x - 3(9x + 6) = 28.
3. Simplify the equation: 4x - 27x - 18 = 28.
4. Combine like terms: -23x - 18 = 28.
5. Add 18 to both sides: -23x = 46.
6. Divide by -23: x = -2.
7. Substitute this value of x back into either equation to find y.

Method 2: Elimination

1. Multiply the second equation by 3 to make the coefficients of y the same: 27x - 3y = -18.
2. Add this equation to the first equation to eliminate y: (4x - 3y) + (27x - 3y) = 28 + (-18).
3. Simplify the equation: 31x = 10.
4. Divide by 31: x = 10/31.
5. Substitute this value of x back into either equation to find y.

Therefore, the solution to the system of equations is x = -2 and y = 6.