What is the solution to the system of equations?

Enter your answer as the correct ordered pair, like this:

Ask by Jimenez Hardy. in the United States

Jan 31,2025

Question

What is the solution to the system of equations? $$ \left\{\begin{array}{l}y=5 x-10 \ y=-3 x+14\end{array}ight. $$ Enter your answer as the correct ordered pair, like this: $$ (42,53) $$

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
y = 5x - 10 \
y = -3x + 14
\end{cases}
$$

**Step 1:** Set the two equations equal to each other since both are equal to $$ y $$:

$$
5x - 10 = -3x + 14
$$

**Step 2:** Combine like terms:

$$
5x + 3x = 14 + 10 \
8x = 24
$$

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

$$
x = \frac{24}{8} = 3
$$

**Step 4:** Substitute $$ x = 3 $$ back into one of the original equations to find $$ y $$. Using $$ y = 5x - 10 $$:

$$
y = 5(3) - 10 = 15 - 10 = 5
$$

**Solution:**

$$
(3,5)
$$
The solution is $$ (3, 5) $$.

What is the solution to the system of equations?

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