QuestionDecember 25, 2025

15. Create a system of linear equations and tell me what the solution is.

15. Create a system of linear equations and tell me what the solution is.
15. Create a system of linear equations and tell me what the solution is.

Solution
4.2(255 votes)

Answer

The solution is x = \frac{8}{3}, y = \frac{5}{3}. Explanation 1. Create the system Let’s choose two equations: 2x + y = 7 and x - y = 1. 2. Solve for one variable Add both equations: (2x + y) + (x - y) = 7 + 1 \implies 3x = 8 \implies x = \frac{8}{3}. 3. Substitute to find the other variable Substitute x into x - y = 1: \frac{8}{3} - y = 1 \implies y = \frac{8}{3} - 1 = \frac{5}{3}.

Explanation

1. Create the system<br /> Let’s choose two equations: $2x + y = 7$ and $x - y = 1$.<br />2. Solve for one variable<br /> Add both equations: $(2x + y) + (x - y) = 7 + 1 \implies 3x = 8 \implies x = \frac{8}{3}$.<br />3. Substitute to find the other variable<br /> Substitute $x$ into $x - y = 1$: $\frac{8}{3} - y = 1 \implies y = \frac{8}{3} - 1 = \frac{5}{3}$.
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