Question

solve by elimination: 4x + 9y = 28 -4x - y = -28

Explanation:

Step1: Add the two equations

We have the system of equations:

$$\begin{cases} 4x + 9y = 28 \\ -4x - y = -28 \end{cases}$$

Adding the left - hand sides and the right - hand sides of the two equations respectively:
$(4x + 9y)+(-4x - y)=28+(-28)$
Simplify the left - hand side: $4x-4x + 9y-y=8y$
Simplify the right - hand side: $28 - 28 = 0$
So we get the equation $8y=0$

Step2: Solve for y

From $8y = 0$, divide both sides by 8:
$y=\frac{0}{8}=0$

Step3: Substitute y = 0 into one of the original equations

Substitute $y = 0$ into the first equation $4x+9y = 28$:
$4x+9\times0=28$
Simplify: $4x=28$

Step4: Solve for x

Divide both sides of $4x = 28$ by 4:
$x=\frac{28}{4}=7$

Answer:

The solution to the system of equations is $(7,0)$