Question

-2x+3y=14 and x+2y=7 what is the value of x and y

Answer 1

The solution to the system of equations is x = -1 and y = 4, found by using the elimination method to first eliminate x and then solve for y, and subsequently solve for x.

Step-by-step explanation:

To solve the system of equations, we can use either the substitution method or the elimination method. Given the two equations:

• -2x + 3y = 14
• x + 2y = 7

Let's use the elimination method. First, we will multiply the second equation by 2 to align the coefficients for the y terms:

2(x + 2y) = 2×7

2x + 4y = 14

Now, we have the modified system:

• -2x + 3y = 14
• 2x + 4y = 14

Adding the two equations to eliminate x:

-2x + 3y + 2x + 4y = 14 + 14

7y = 28

y = 28 / 7

y = 4

Now, substitute y = 4 into one of the original equations to find x:

x + 2×4 = 7

x + 8 = 7

x = 7 - 8

x = -1

Thus, the solution to the system of equations is x = -1 and y = 4.