Use elimination to solve the system of equations.

Ask by Hamilton Rojas. in the United States

Mar 25,2025

Question

Use elimination to solve the system of equations. $$ 13 x+14 y=59 $$ $$ 4 x+7 y=37 $$

UpStudy AI · Accepted Answer

**Step 1: Write down the system of equations.**

$$
13x + 14y = 59
$$
$$
4x + 7y = 37
$$

**Step 2: Multiply the second equation by 2 so that the coefficients of $$ y $$ match.**

Multiplying the second equation by 2 gives:

$$
2(4x + 7y) = 2(37) \quad \Rightarrow \quad 8x + 14y = 74
$$

**Step 3: Subtract the new equation from the first equation to eliminate $$ y $$.**

Subtracting:

$$
(13x + 14y) - (8x + 14y) = 59 - 74
$$
$$
(13x - 8x) + (14y - 14y) = -15
$$
$$
5x = -15
$$

**Step 4: Solve for $$ x $$.**

$$
x = \frac{-15}{5} = -3
$$

**Step 5: Substitute $$ x = -3 $$ back into one of the original equations to solve for $$ y $$.**

Using the second equation:

$$
4x + 7y = 37
$$
$$
4(-3) + 7y = 37
$$
$$
-12 + 7y = 37
$$
$$
7y = 37 + 12
$$
$$
7y = 49
$$
$$
y = \frac{49}{7} = 7
$$

**Final Answer:**

$$
x = -3, \quad y = 7
$$
$$ x = -3 $$ and $$ y = 7 $$.

Use elimination to solve the system of equations.