Use elimination to solve the system of equations.

Ask by Fernandez Sherman. 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: Multiply the second equation by 2**

We have the system:
$$
13x + 14y = 59
$$
$$
4x + 7y = 37
$$

Multiply the second equation by $$2$$ so that the coefficient of $$y$$ matches the first equation:
$$
2 \times (4x + 7y) = 2 \times 37 \quad \Longrightarrow \quad 8x + 14y = 74
$$

**Step 2: Subtract the new equation from the first equation**

Subtract the equation $$8x + 14y = 74$$ from the first equation:
$$
(13x + 14y) - (8x + 14y) = 59 - 74
$$
$$
13x - 8x = -15
$$
$$
5x = -15
$$

**Step 3: Solve for $$x$$**

Divide both sides by $$5$$:
$$
x = \frac{-15}{5} = -3
$$

**Step 4: Substitute $$x = -3$$ into one of the original equations to solve for $$y$$**

Using the second equation:
$$
4x + 7y = 37
$$
Substitute $$x = -3$$:
$$
4(-3) + 7y = 37
$$
$$
-12 + 7y = 37
$$

**Step 5: Solve for $$y$$**

Add $$12$$ to both sides:
$$
7y = 37 + 12
$$
$$
7y = 49
$$
Divide both sides by $$7$$:
$$
y = \frac{49}{7} = 7
$$

**Final Answer:**
$$
x = -3, \quad y = 7
$$
$$ x = -3 $$ and $$ y = 7 $$.

Use elimination to solve the system of equations.

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