Question

1. what does the solution to a system of linear equations represent?

a. the slope of the line
b. the point where the equations intersect
c. the y-intercept of the line
d. the maximum value of the function

1. in the system $y = 3x + 5$ and $2x + y = 10$, what is the value of $x$ after substitution?

a. 2
b. -1
c. 0
d. 1

Explanation:

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First Question

Step1: Recall system solution definition

A system of linear equations' solution is the set of values that satisfy all equations in the system, which corresponds to the intersection point of the lines (in 2D).
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Second Question

Step1: Substitute $y=3x+5$ into $2x+y=10$

$2x + (3x + 5) = 10$

Step2: Simplify the equation

$2x + 3x + 5 = 10 \implies 5x + 5 = 10$

Step3: Isolate the term with $x$

$5x = 10 - 5 \implies 5x = 5$

Step4: Solve for $x$

$x = \frac{5}{5} = 1$

Answer:

1. b. The point where the equations intersect
2. d. 1