𝑁 is the point of intersection of the lines with equations 2𝑥−𝑦=−9 and 3𝑥+5𝑦=−7Write down the coordinates of 𝑁.
Question
𝑁 is the point of intersection of the lines with equations 2𝑥−𝑦=−9 and 3𝑥+5𝑦=−7Write down the coordinates of 𝑁.
Solution
To find the point of intersection of the two lines, we need to solve the system of equations given by the two lines. The system of equations is:
2x - y = -9 3x + 5y = -7
Step 1: Solve one of the equations for one variable.
Let's solve the first equation for y:
2x - y = -9 => y = 2x + 9
Step 2: Substitute the expression for y from the first equation into the second equation:
3x + 5(2x + 9) = -7 => 3x + 10x + 45 = -7 => 13x + 45 = -7 => 13x = -52 => x = -52 / 13 => x = -4
Step 3: Substitute x = -4 into the first equation to solve for y:
y = 2(-4) + 9 => y = -8 + 9 => y = 1
So, the point of intersection N is (-4, 1).
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