Question

Estimate the intersection point of the graphs of the following linear equations in two variables.

y=−x+7
𝑦
=
−
𝑥
+
7

y=4x−3
𝑦
=
4
𝑥
−
3



(
(
, )
)
Check answer

Answer 1

To find the intersection point of the graphs of the two equations, we will set them equal to each other and solve for \(x\).

The equations are:
1. \(y = -x + 7\)
2. \(y = 4x - 3\)

Setting them equal to each other:

\[
-x + 7 = 4x - 3
\]

Now, let's solve for \(x\):

1. Add \(x\) to both sides:

\[
7 = 5x - 3
\]

2. Add \(3\) to both sides:

\[
10 = 5x
\]

3. Divide both sides by \(5\):

\[
x = 2
\]

Now that we have \(x\), we'll substitute it back into one of the original equations to find \(y\). We'll use the first equation:

\[
y = -x + 7
\]
\[
y = -2 + 7
\]
\[
y = 5
\]

Thus, the intersection point of the graphs of the two equations is \((2, 5)\).

**Check the answer**:

Let's check this point in the second equation:

\[
y = 4x - 3
\]
Substituting \(x = 2\):

\[
y = 4(2) - 3
\]
\[
y = 8 - 3
\]
\[
y = 5
\]

Since the point \((2, 5)\) satisfies both equations, we confirm that the intersection point is indeed:

\[
\boxed{(2, 5)}
\]