show how to solve these problems:

Question

1.  6x - y = -4
    2x + 2y = 15    answer:x = 1/2
                           y = 7

2.  x +y = 1               x = -1/3
    2x - y = -2            y = 4/3

3.  x - y = 3              x = 5/2
    6x + 4y = 13           y = - 1/2

I just need to know how to solve these problems. Please show me how it is done.

drwls · Answer

Do them all the same way: either by combining equations in a way that cancels out one unknown, or by substitution. Here is how problem #3 can be solved: Substitute y + 3 for x in the second equation, 6(y+3)+ 4y = 13 10y + 18 = 13 10 y = -5 y = -1/2 x = y+3 = 5/2 Now you try the others.

Explain Bot · Answer

To solve these problems, you can use the method of substitution or elimination. I will demonstrate the process using the method of substitution for each problem: 1. Problem: 6x - y = -4 (Equation 1) 2x + 2y = 15 (Equation 2) Step 1: Solve Equation 1 for one variable (in terms of the other variable). 6x - y = -4 y = 6x + 4 (Equation 3) Step 2: Substitute Equation 3 into Equation 2. 2x + 2(6x + 4) = 15 2x + 12x + 8 = 15 14x + 8 = 15 Step 3: Solve for x. 14x = 15 - 8 14x = 7 x = 7/14 x = 1/2 Step 4: Substitute the value of x back into Equation 3 to find y. y = 6(1/2) + 4 y = 3 + 4 y = 7 Therefore, the solution is x = 1/2 and y = 7. 2. Problem: x + y = 1 (Equation 1) 2x - y = -2 (Equation 2) Step 1: Solve Equation 1 for one variable. x + y = 1 x = 1 - y (Equation 3) Step 2: Substitute Equation 3 into Equation 2. 2(1 - y) - y = -2 2 - 2y - y = -2 2 - 3y = -2 Step 3: Solve for y. 2 - 3y = -2 -3y = -2 - 2 -3y = -4 y = -4/(-3) y = 4/3 Step 4: Substitute the value of y back into Equation 3 to find x. x = 1 - (4/3) x = 3/3 - 4/3 x = -1/3 Therefore, the solution is x = -1/3 and y = 4/3. 3. Problem: x - y = 3 (Equation 1) 6x + 4y = 13 (Equation 2) Step 1: Solve Equation 1 for one variable. x - y = 3 x = y + 3 (Equation 3) Step 2: Substitute Equation 3 into Equation 2. 6(y + 3) + 4y = 13 6y + 18 + 4y = 13 10y + 18 = 13 Step 3: Solve for y. 10y + 18 = 13 10y = 13 - 18 10y = -5 y = -5/10 y = -1/2 Step 4: Substitute the value of y back into Equation 3 to find x. x = (-1/2) + 3 x = -1/2 + 6/2 x = 5/2 Therefore, the solution is x = 5/2 and y = -1/2. I hope this helps! Let me know if you have any further questions.