Question

Solve this system of linear equations. Separate

the x- and y-values with a comma.
9x + 2y = -14
-14x + 5y = 38
a) x = -2, y = 5

b) x = 3, y = -4

c) x = -4, y = 3

d) x = 5, y = 2

Answer 1

To solve the system, the elimination method was used to cancel out the variable x and find y = 2. Substituting y back into the original equation, x = -2. The solution is x = -2, y = 2.

Step-by-step explanation:

To solve the system of linear equations:
9x + 2y = -14
-14x + 5y = 38

We can use the method of substitution or elimination. In this case, we will use elimination. We want to eliminate one of the variables, let's pick x for this example. To eliminate x, we can multiply the first equation by 14 and the second equation by 9, then add them together to cancel out x:

• (14)(9x + 2y) = (14)(-14)
• (9)(-14x + 5y) = (9)(38)

Doing the algebraic operations, we get:

• 126x + 28y = -196
• -126x + 45y = 342

Adding these together, x cancels and we are left with:

28y + 45y = -196 + 342

73y = 146

y = 146 / 73 = 2

Now that we have y, we can substitute back into one of the original equations to solve for x:

9x + 2(2) = -14

9x + 4 = -14

9x = -18

x = -18 / 9 = -2

Therefore, the solution is x = -2, y = 2.